CN105337702A

CN105337702A - Network transmission method adopting spatial network coding based on Delaunay triangulation

Info

Publication number: CN105337702A
Application number: CN201510652168.5A
Authority: CN
Inventors: 黄佳庆; 李宗鹏
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2015-10-10
Filing date: 2015-10-10
Publication date: 2016-02-17
Anticipated expiration: 2035-10-10
Also published as: CN105337702B

Abstract

The invention discloses a network transmission method adopting spatial network coding based on Delaunay triangulation. The method is suitable for a transmission network including N terminal points. The method comprises an initialization step, a Delaunay preprocessing step, a sub-rectangle formation step, a sub-rectangle division step, a step for solving linear programming optimum solution before balance, a step for adjusting a relay point to a balance position, a step for solving linear programming optimum solution after balance and a Delaunay post-processing step. Steiner points and supplemental Steiner points are obtained through Delaunay triangulation and serve as candidate relay points, and the candidate relay points are obtained through non-uniform division; the optimal relay point is selected from the candidate relay points above; and the position of the selected relay point is adjusted slightly to further reduce cost, thereby obtaining a network transmission scheme adopting the spatial network coding, solving the problem that, in a spatial network coding method only based on non-uniform division in the prior art, when the relay points and termination points are in non-uniform density distribution, calculation amount is large when solving the linear programming optimum solution, and furthermore, improving the overall performance of network transmission effectively.

Description

A kind of network transfer method adopting the spatial network based on Delaunay triangulation to encode

Technical field

The invention belongs to network information transfer technical field, more specifically, relate to the network transfer method that a kind of employing is encoded based on the spatial network of Delaunay triangulation.

Background technology

Network code is one of important branch of network information opinion, and its basic thought allows nodes to participate in coding and decoding, can promote throughput, improve bandwidth availability ratio and reduce algorithm complex; Network code theory proposes information flow concept, points out that network code is also referred to as network information flow by coding and decoding compressed information stream to promote throughput.

Spatial network coding study be network code in geometric space, also referred to as spatial information stream.Geometric space refers to Euclidean space herein.Spatial information stream allows to add extra relay point and adjacent links thereof, and aforementioned network information flow does not then allow.The exemplary advantage of spatial network coding adopts the cost of network code can strictly be less than in space the cost adopting route in space; Adopt QoS routing in space, be equivalent to Euclid's Steiner minimal tree problem, this problem verified is nondeterministic polynomial difficulty (NP-Hard) problem, and the method complexity solving this problem is higher; Adopt network code in space, its cost strictly can be less than the cost of the optimum QoS routing in space, and representative instance is five-pointed star network.Visible, there is essential distinction with space route in spatial network coding, and the importance and necessity of research spatial network coding is described; Wherein, relay point refers to the communication node increased for reaching the network service target with minimum cost, and its number and position are arbitrary; For reaching the Internet Transmission with minimum cost, the position range of relay point (should comprise convex closure border) in the determined convex closure of end point; Convex closure refers in two-dimensional space the minimal convex polygon comprising terminal point set.

Consider the network transmission problems adopting spatial network to encode in Euclidean space: for any given end point set, and allow to add extra relay point, communication target is the multicast network that requirement realizes having minimum cost.A kind of network transfer method of the spatial network coding based on evenly dividing is had in prior art, the constraint rectangle that its substance comprises given end point is formed carries out evenly dividing obtaining rectangular grid, get each rectangular grid center relay point alternatively, build complete graph for all end point and relay point, then build the linear programming model based on information flow and ask Optimal Solution of Linear Programming; Progressively increase the quantity evenly divided, required topology approaches optimum topology, finally adopts the method for mechanical balance to solve the optimal location of relay point; Wherein, end point refers to the node that in network service, position is fixing, comprises an information source node and at least one information destination node, is called information source terminal point and destination end point; Complete graph refers to the simple graph having a link between any two points; Simple graph refers to neither have the figure that central link does not exist multilink yet.

The method exists following not enough: when there is non-homogeneous density distribution between given end point and end point, now adopt rectangular grid quantity after evenly dividing very large, when building complete graph, link sum is also very large, and when causing asking Optimal Solution of Linear Programming, amount of calculation increases suddenly.

For the problems referred to above, a kind of network transfer method of encoding based on the spatial network of non-homogeneous division (Non-uniformPartitioning) is had in prior art, its substance comprises and carries out non-homogeneous division to given end point, namely from each terminal strokes and dots horizontal line and vertical line, each bar horizontal line and vertical line intersection point form some sub-rectangles, be p × p rectangular grid by every sub-rectangular partition again, get each rectangular grid center relay point alternatively, relay point for all end point and candidate builds complete graph, then build the linear programming model based on information flow and ask Optimal Solution of Linear Programming, progressively increase the quantity of p, required topology approaches optimum topology, finally adopts the method for mechanical balance to solve the optimal location of relay point.

The method exists following not enough: when there is non-homogeneous density distribution between relay point and end point, after now adopting non-homogeneous division, rectangular grid quantity is very large, when building complete graph, link sum is also very large, and when causing asking Optimal Solution of Linear Programming, amount of calculation increases suddenly.

Summary of the invention

For above defect or the Improvement requirement of prior art, the invention provides the network transfer method that a kind of employing is encoded based on the spatial network of Delaunay triangulation, its object is to solve prior art only based in the spatial network coding method of non-homogeneous division, the problem that when asking Optimal Solution of Linear Programming when relay point and end point non-homogeneous density distribution, amount of calculation is large.

Wherein, Delaunay triangulation (DelaunayTriangulation) refers to that the convex closure subdivision by being formed by end point in two-dimentional Euclidean space is several Delaunay triangles, these Delaunay triangles meet following main character: any one Delaunay triangular apex has and only has a circle, and not containing other end point any (i.e. largest empty circle character) in this circle; Any one Delaunay triangle must be minimum angle maximum (minimum angle maximization principle), and the latter makes Delaunay triangle closer to equilateral triangle.

For achieving the above object, according to one aspect of the present invention, provide the network transfer method that a kind of employing is encoded based on the spatial network of Delaunay triangulation, be applicable to the transmission network comprising N number of end point, N is positive integer; The method comprises initialization step, Delaunay pre-treatment step, forms sub-rectangle step, sub-rectangular partition step, ask the frontal planning optimal solution step of balance, adjustment relay point to equilbrium position step, ask balance Optimal Solution of Linear Programming step and Delaunay post-processing step afterwards, specific as follows:

(1) initialization step: the convex closure calculating N number of end point, obtains each bar limit of the minimal convex polygon comprising each end point; Wherein, convex closure refers in two-dimensional space the minimal convex polygon comprising terminal point set; N is positive integer;

(2) Delaunay pre-treatment step: for N number of end point, adopts the method for Delaunay triangulation to obtain (2N-5) individual Delaunay triangle at the most; Adopt the method for the stainer point of calculating 3 end point, obtain the leg-of-mutton stainer point of each Delaunay; Every two adjacent Delaunay triangles are spliced into a quadrangle, adopt the method for the stainer point of calculating 4 end point, obtain the stainer point of each quadrangle; By all stainer points stored in stainer point S set;

(3) sub-rectangle step is formed: the maximum YA obtaining the minimum value XI of the abscissa of N number of end point coordinate, the maximum XA of abscissa, the minimum value YI of ordinate and ordinate; Connection coordinate is (XI, y _k) and (XA, y _k) 2 points, form horizontal line section; Connection coordinate is (x _k, YI) and (x _k, YA) 2 points, form ordinate section; Each horizontal line section and ordinate section form sub-rectangle; Wherein, (x _k, y _k) be end point t _kcoordinate, 0≤k≤N-1;

(4) sub-rectangular partition step: be p × p rectangular grid by each sub-rectangular partition, obtains the coordinate of each rectangular grid diagonal intersection point; Obtain all diagonal intersection points be positioned at convex closure on convex closure, by these intersection points relay point alternatively, stored in relay point set R;

Complete graph K=(V, E, ω (uv)) is built to end point set, the set of stainer point, relay point set, supplement stainer point set and current optimum relay point union of sets collection;

Wherein, front nodal point set V=T ∪ S ∪ S ' ∪ R ∪ R is balanced ^*, comprise N=|T| end point and M=|S ∪ S ' ∪ R ∪ R ^*| the relay point r of individual candidate _n-1+m, r _n-1+mcoordinate be (x _n-1+m, y _n-1+m), 1≤m≤M; Connect with undirected link uv between any two node u and v in node set V, uv ∈ E, E refer to the set of all undirected links; The weights ω (uv) of undirected link uv is the Euclidean distance between two node u and v; P gets the positive integer being not less than 2; T refers to the end point set be made up of N number of end point; S refers to the set of stainer point; S ' refers to the set of supplement stainer point; R refers to relay point set; R ^*refer to current optimum relay point set;

(5) ask the frontal planning optimal solution step of balance: based on above-mentioned complete graph K, build the front linear programming model based on information flow of balance, comprise target function and constraints;

Target function is constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition; Utilize linear programming method to obtain the front optimal solution based on the linear programming model of information flow of balance, export the target function value C based on the linear programming model of information flow before balancing _p; Export each directed link the rate of information throughput value and total information transmission rate value, and the value of the total information transmission rate f (uv) of each undirected link uv;

Judge whether to meet C _p< CI; If so, then by target function value C _pas minimum cost value CI before balance; If not, then whether the total information transmission rate judging the undirected link of all of its neighbor of all relay points is zero entirely;

If so, show non-relay point, then put current optimum relay point set R ^*for empty set, and enter step (7); If not, be not then the relay point of zero entirely for the total information transmission rate of the adjacent undirected link of relay point, judge whether that wherein more than 2 relay points are on a line segment; If, then delete other relay point be on this line segment, only retain 2 relay points being in this line segment point position, search the relay point of satisfied " the total information transmission rate of the undirected link of its all of its neighbor is not zero entirely ", and will all relay points of this condition be met stored in current optimum relay point set R ^*, enter step (6); Wherein, R is gathered ^*size be M ^*, be designated as M ^*=| R ^*|; refer to the front directed link of balance weights, be the Euclidean distance between two node u and v; A refers to the front directed link set of balance; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; I is destination end point counter, 1≤i≤N-1;

(6) relay point is adjusted to equilbrium position step: put back counter RD=1; Vectorial addition is adopted to obtain current optimum relay point set R ^*in each relay point r _n-1+jmake a concerted effort wherein, for the adjacent directed link in edge the power in direction, size if certain relay point does not meet with joint efforts by this relay point r _n-1+jmake a concerted effort along it direction move to its make a concerted effort at ε ₁equilbrium position in scope, until all relay points are made a concerted effort by current optimum set of relay nodes R ^*be updated to all relay points adjusting to equilbrium position, enter step (7); Wherein, for relay point r _n-1+jmake a concerted effort size, ε ₁for error of making a concerted effort;

(7) Optimal Solution of Linear Programming step after asking balance: build the rear complete graph K of balance ^*=(V ^*, E ^*, ω ^*(u ' v ')); Wherein, posterior nodal point set V is balanced ^*=T ∪ R ^*, by N number of end point and M ^*individually adjust to the relay point behind equilbrium position and form, balance posterior nodal point set V ^*in connect with undirected link u ' v ' between any two node u ' and v ', u ' v ' ∈ E ^*, E ^*refer to the set of all undirected links; The weights ω of undirected link u ' v ' ^*(u ' v ') is the Euclidean distance between two node u ' and v ';

Based on complete graph K after balance ^*, build the linear programming model based on information flow after balancing, its target function is its constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition; Utilize linear programming method to obtain the rear Optimal Solution of Linear Programming of balance, export the target function value after balance each directed link after balance the rate of information throughput with total information transmission rate numerical value;

Wherein, refer to directed link weights, be the Euclidean distance between two node u ' and v '; A ^*refer to the rear directed link set of balance; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput, 1≤i≤N-1;

Judge whether to meet if so, then by the target function value after balance as minimum cost value CI after balance ^*;

If not, then satisfied 0≤CI-CI is judged whether ^*≤ ε ₂; If not, put p=p+1, enter step (4);

If so, satisfied 0≤CL is then judged whether ^*-CI ^*≤ ε ₃, if so, enter step (8); If not, then the minimum cost value CL last round of balance obtained afterwards ^*as minimum cost value CI after balance ^*, juxtaposition p=p+1, enters step (4); Wherein, ε ₂refer to the first cost error, ε ₃refer to the second cost error;

(8) Delaunay post-processing step: search with end point t _kfor all angles that any two links of public vertex are formed; Adopt the method for the stainer point of calculating 3 end point, obtain the stainer point that the angle formed is less than three summits of 120 °, stored in supplement stainer point S set ';

Judge supplement stainer point S set ' whether be empty set, if not, enter step (4); If so, show to find the Internet Transmission mode with minimum cost, then export the rear each directed link of balance the rate of information throughput with total information transmission rate value, balance after minimum cost value CI ^*, and current optimum relay point set R ^*in relay point coordinate; Wherein, k is end point counter, 0≤k≤N-1.

Preferably, the Delaunay pre-treatment step of above-mentioned steps (2), comprises following sub-step:

(2.1) for N number of end point, the method for Delaunay triangulation is adopted to obtain (2N-5) individual Delaunay triangle at the most;

(2.2) adopt the method for the stainer point of calculating 3 end point, obtain the leg-of-mutton stainer point of each Delaunay, by all stainer points of obtaining stored in stainer point S set;

(2.3) every two adjacent Delaunay triangles are spliced into a quadrangle, adopt the method for the stainer point of calculating 4 end point, obtain the stainer point of each quadrangle; By all stainer points of obtaining also stored in stainer point S set.

Preferably, above-mentioned steps (3) forms sub-rectangle step, comprises following sub-step:

(3.1) end point counter k=0 is put;

(3.2) judge whether to meet k≤N-1; If so, enter sub-step (3.3), if not, then enter sub-step (3.5);

(3.3) obtain the maximum YA of minimum value XI, the maximum XA of abscissa of the abscissa of N number of end point coordinate, the minimum value YI of ordinate and ordinate, comprise following process:

(3.3.1) judge whether to meet XI>x _k, be put XI=x _k, then enter (3.3.2); Otherwise directly enter (3.3.2);

(3.3.2) judge whether to meet YI>y _k, be put YI=y _k, then enter (3.3.3); Otherwise directly enter (3.3.3);

(3.3.3) judge whether to meet XA<x _k, be put XA=x _k, then enter (3.3.4); Otherwise directly enter (3.3.4);

(3.3.4) judge whether to meet YA<y _k, be put YA=y _k, then enter sub-step (3.4); Otherwise directly enter sub-step (3.4);

(3.4) put k=k+1, and be back to sub-step (3.2);

(3.5) empty end point counter, put k=0;

(3.6) judge whether to meet k≤N-1; If so, sub-step (3.7) is then entered; If not, then sub-step (3.9) is entered;

(3.7) connection coordinate is (XI, y _k) and (XA, y _k) 2 points, form horizontal line section; Connection coordinate is (x _k, YI) and (x _k, YA) 2 points, form ordinate section;

(3.8) put k=k+1, enter sub-step (3.6);

(3.9) each horizontal line section and ordinate section form sub-rectangle; Wherein, (x _k, y _k) be end point t _kcoordinate, put initial value XI=+ ∞, XA=-∞, YI=+ ∞, YA=-∞.

Preferably, the sub-rectangular partition step of above-mentioned (4), comprises following sub-step:

(4.1) be p × p rectangular grid by each sub-rectangular partition that step (3) obtains, obtain the coordinate of each rectangular grid diagonal intersection point;

(4.2) adopt point localization method, find be positioned at described convex closure and all rectangular grid diagonal intersection points, by above-mentioned intersection point relay point alternatively, stored in relay point set R;

(4.3) complete graph K=(V, E, ω (uv)) is built, node set V=T ∪ S ∪ S ' ∪ R ∪ R ^*, comprise N=|T| end point and M=|S ∪ S ' ∪ R ∪ R ^*| the relay point r of individual candidate _n-1+m, wherein r _n-1+mcoordinate be (x _n-1+m, y _n-1+m), m is relay point counter before balance; 1≤m≤M;

Wherein, connect with undirected link uv between any two node u and v in node set V, uv ∈ E, E refer to the set of all undirected links; The weights ω (uv) of undirected link uv is the Euclidean distance between two node u and v; T refers to the end point set be made up of N number of end point; S refers to the set of stainer point; S ' refers to the set of supplement stainer point; R refers to the set of candidate relay point; R ^*refer to current optimum relay point set; Put initial value S ' and R ^*for empty set.

Preferably, asking of step (5) balances frontal planning optimal solution step, comprises following sub-step:

(5.1) based on the complete graph K that step (4) obtains, build the front linear programming model based on information flow of balance, comprise target function and constraints;

Target function is target function wherein, directed link set decision variable is directed link in complete graph K total information transmission rate decision variable coefficient

Constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition:

Information flow conservation condition:

Information flow upper bound condition:

Non-negative condition:

(5.2) utilize linear programming method to obtain the front optimal solution based on the linear programming model of information flow of described balance, export the front target function value C based on the linear programming model of information flow of described balance _p; Export each directed link the rate of information throughput with total information transmission rate value and the value of total information transmission rate f (uv) of each undirected link uv; Wherein,

(5.3) judge whether target function value meets C _p<CI; If so, then by target function value C _pas minimum cost value CI before balance, enter sub-step (5.4); If not, then sub-step (5.4) is directly entered;

(5.4) whether the total information transmission rate judging the undirected link of all of its neighbor of all relay points is zero entirely; If so, current optimum relay point set R is then put ^*for empty set, enter step (7); If not, then sub-step (5.5) is entered;

(5.5) for the total information transmission rate of the adjacent undirected link of relay point be not entirely zero relay point, judge whether that wherein more than 2 relay points are on a line segment; If so, then only retain 2 relay points being in this line segment endpoint location, enter sub-step (5.6); If not, then sub-step (5.6) is directly entered;

(5.6) search the relay point of satisfied " the total information transmission rate of the undirected link of its all of its neighbor is not zero entirely ", and will all relay points of described condition be met stored in current optimum relay point set R ^*, the size of described current optimum relay point set is M ^*, be designated as M ^*=| R ^*|;

Wherein, 1≤i≤N-1; U, v, t ₀, t _i∈ V, v _←u () represents that beginning node is the set of all directed link terminal notes of u, V _→u () represents that terminal note is the set of all directed link beginning nodes of u; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; for directed link on total information transmission rate, it equals directed link upper all maximum; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; H is the total information transmission rate that information source sends, h>0; Put initial value CI=+ ∞.

Preferably, the adjustment relay point of step (6), to equilbrium position step, comprises following sub-step:

(6.1) counter RD=1 is put back;

(6.2) relay point variable j=1 is put, horizontalization weighing apparatus counter BL=0;

(6.3) vectorial addition is adopted to calculate relay point r _n-1+jmake a concerted effort wherein, for the adjacent directed link in edge the power in direction, size

(6.4) judge whether to meet if so, then put BL=BL+1, enter sub-step (6.5); If not, then by relay point r _n-1+jmake a concerted effort along it displacement Δ=1/, direction (2 × RD+3), put enter sub-step (6.5) again; Wherein, for relay point r _n-1+jmake a concerted effort size, ε ₁for error of making a concerted effort;

(6.5) put j=j+1, judge whether to meet j≤M ^*; If so, sub-step (6.3) is then entered; If not, then sub-step (6.6) is entered;

(6.6) judge whether to meet BL=M ^*, if so, then show that all relay points adjust to equilbrium position, by current optimum set of relay nodes R ^*be updated to all relay points adjusting to equilbrium position, enter step (7); If not, then put RD=RD+1, enter sub-step (6.2).

Preferably, asking of step (7) balances rear Optimal Solution of Linear Programming step, comprises following sub-step:

(7.1) the rear complete graph K of balance is built ^*=(V ^*, E ^*, ω ^*(u ' v ')), node set V ^*=T ∪ R ^*, comprise N number of end point and M ^*individually adjust to the relay point behind equilbrium position, node set V ^*in connect with undirected link u ' v ' between any two node u ' and v ', u ' v ' ∈ E ^*;

(7.2) based on complete graph K after described balance ^*, build the linear programming model based on information flow after balancing, this model is made up of target function and constraints;

Target function is wherein, directed link set decision variable is complete graph K ^*middle directed link total information transmission rate decision variable coefficient

Information flow conservation condition:

Information flow upper bound condition:

Non-negative condition:

(7.3) based on the optimal solution of the linear programming model of information flow after utilizing linear programming method acquisition to balance, the target function value after balance is exported export each directed link the rate of information throughput with total information transmission rate value;

(7.4) target function value after described balance is judged whether meet if so, then horizontalization weighing apparatus after minimum cost value enter sub-step (7.5); If not, then sub-step (7.5) is directly entered;

(7.5) satisfied 0≤CI-CI is judged whether ^*≤ ε ₂; If so, sub-step (7.6) is then entered; If not, then put p=p+1, enter step (4);

(7.6) satisfied 0≤CL is judged whether ^*-CI ^*≤ ε ₃; If so, step (8) is then entered; If not, then minimum cost value CL after last round of balance is put ^*=CI ^*, put p=p+1, enter step (4);

Wherein, E ^*refer to the set of all undirected links; The weights ω of undirected link u ' v ' ^*(u ' v ') is the Euclidean distance between node u ' and v '; 1≤i≤N-1; U ', v ', t ₀, t _i∈ V ^*, refer to that beginning node is the set of all directed link terminal notes of u ', refer to that terminal note is the set of all directed link beginning nodes of u '; refer to from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; for directed link on total information transmission rate, equal directed link upper all maximum; refer to from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; H is the total information transmission rate that information source sends, h>0; ε ₂be the first cost error, ε ₃it is the second cost error; Put initial value CI ^*=+∞, CL ^*=+∞.

Preferably, the Delaunay post-processing step of step (8), comprises following sub-step:

(8.1) end point counter k=0 is put;

(8.2) search with end point t _kfor all angles that any two links of public vertex are formed;

(8.3) judge whether described angle is less than 120 °; If so, then adopt the method for the stainer point of calculating 3 end point, obtain often group and form the stainer point on three summits of above-mentioned angle; By all stainer points obtained stored in augmenting stainer point S set ' in, enter sub-step (8.4); If not, then sub-step (8.4) is entered;

(8.4) judge whether to meet k=N-1; If so, sub-step (8.5) is then entered; If not, then put k=k+1, enter sub-step (8.2);

(8.5) judge whether S ' is empty set; If so, show to find the Internet Transmission mode with minimum cost, then export CI ^*, all nonzero information transmission rates with non-zero total information transmission rate value, and export current optimum relay point set R ^*in relay point coordinate; If not, then step (4) is entered;

Preferably, the above-mentioned error ε that makes a concerted effort ₁meet 0≤ε ₁≤ 0.0001; ε ₁less, the position of relay point is more accurate, but computing time is longer.

Preferably, above-mentioned first cost error meets 0≤ε ₂≤ 0.0001, above-mentioned second cost error ε ₃meet 0≤ε ₃≤ 0.0001; ε ₂and ε ₃it is less, with more accurate, but computing time is longer.

The convex closure of end point is obtained by above-mentioned step (1); Adopt Delaunay triangulation to obtain Delaunay triangle by step (2), then obtain all Delaunay leg-of-mutton stainer point and all two adjacent Delaunay triangles form the stainer point of quadrangle; By step (3) and step (4), convex closure is carried out the relay point that non-homogeneous division obtains candidate: step (3) obtains the sub-rectangle of end point, step (4) is p × p rectangular grid to every sub-rectangle Further Division, is taken at the diagonal intersection point relay point alternatively with the rectangular grid in convex closure on convex closure; Complete graph is built to end point, stainer point, candidate relay point, supplement stainer point and current optimum relay point; Build the front linear programming model based on information flow of balance by step (5), ask the frontal planning optimal solution of balance, export the rate of information throughput of each directed link with total information transmission rate numerical value, and balance before minimum cost value CI; By step (6) position of all current optimum relay points adjusted to make a concerted effort be zero equilbrium position, thus reduce cost further; By the linear programming model based on information flow after step (7) structure balance, obtain the rear Optimal Solution of Linear Programming of balance, export the rate of information throughput of each directed link with total information transmission rate numerical value, and balance after minimum cost value CI ^*, and by current C I ^*be saved to minimum cost value CL after last round of balance ^*; If do not meet 0≤CI-CI ^*≤ ε ₂, then step (4) is re-executed after putting p=p+1; If do not meet 0≤CL ^*-CI ^*≤ ε ₃, then step (4) is re-executed after putting p=p+1; Until enter step (8) after meeting aforementioned two inequality; Supplement stainer point relay point is alternatively calculated stored in supplement stainer point S set by step (8) ' in, if S ' is not empty set, re-execute step (4); If S ' is empty set, export the rate of information throughput of each directed link with total information transmission rate numerical value, and balance after minimum cost value CI ^*, and export current optimum relay point set R ^*in relay point coordinate.

In general, the above technical scheme conceived by the present invention compared with prior art, can obtain following beneficial effect:

1, network transfer method provided by the invention, adopts step (2) Delaunay preprocess method to calculate institute's likely stainer point of any 3 and 4 end point; Adopt step (8) Delaunay post-processing approach, and combine by adjusting balance method with step (5) linear programming method and step (6), calculate the institute's likely stainer point being more than or equal to arbitrarily 5 end point, wherein adopt adjustment relay point in step (6) to the position of the method fine setting relay point of equilbrium position to reduce cost further.Owing to adopting above-mentioned Delaunay preprocess method and Delaunay post-processing approach, only based in the spatial network coding method of non-homogeneous division in solution prior art, ask when relay point and end point exist non-homogeneous density distribution during Optimal Solution of Linear Programming and calculate the large problem of quantitative change.

2, network transfer method provided by the invention, step (2) and the Delaunay Methods and steps (3) of (8) and the non-homogeneous division of (4) are combined, not only can solve cause when end point and end point exist non-homogeneous density distribution ask the problem that the calculating quantitative change of Optimal Solution of Linear Programming is large, and can solve cause when relay point and end point exist non-homogeneous density distribution ask the problem that the calculating quantitative change of Optimal Solution of Linear Programming is large; Solve in step (5) and add the last round of optimal result asking the rear Optimal Solution of Linear Programming gained of balance when previous round Optimal Solution of Linear Programming, the iteration speed finding optimal solution can be accelerated further; Comprehensively aforementioned in steps, the network transmission scheme of the coding of the spatial network based on Delaunay triangulation provided by the invention, its cost is not higher than the network transmission scheme adopting space route, and complexity is lower than the network transmission scheme adopting space route, thus effectively promote the overall performance of Internet Transmission.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of network transfer method provided by the invention;

Fig. 2 is the schematic flow sheet of Delaunay pre-treatment step;

Fig. 3 is the schematic flow sheet forming sub-rectangle step;

Fig. 4 is the schematic flow sheet of sub-rectangular partition step;

Fig. 5 asks the schematic flow sheet balancing frontal planning optimal solution step;

Fig. 6 is the schematic flow sheet of adjustment relay point to equilbrium position step;

Fig. 7 is the schematic flow sheet asking the rear Optimal Solution of Linear Programming step of balance;

Fig. 8 is the schematic flow sheet of Delaunay post-processing step;

Fig. 9 is the result that the embodiment of the present invention adopts network transfer method provided by the invention and obtains.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.In addition, if below in described each execution mode of the present invention involved technical characteristic do not form conflict each other and just can mutually combine.

A kind of network transfer method adopting the spatial network based on Delaunay triangulation to encode provided by the present invention, its flow process as shown in Figure 1, comprises initialization step, Delaunay pre-treatment step, forms sub-rectangle step, sub-rectangular partition step, asks the frontal planning optimal solution step of balance, adjustment relay point to equilbrium position step, asks balance afterwards Optimal Solution of Linear Programming step and Delaunay post-processing step; Specifically set forth below in conjunction with embodiment;

Embodiment is for comprising the transmission network of N=5 end point, the coordinate of end point is respectively (0.5415756,0.4475305), (0.1177682,0.4999264), (0.2681085,0.3512345), (0.6861621,0.0972497) and (0.9908014,0.3454797); Wherein (0.5415756,0.4475305) coordinate that is information source terminal point, Internet Transmission target be information source terminal point with minimum cost message transfer to all the other 4 destination end points; The network transfer method that embodiment provides, specific as follows:

(1) initialization step: calculate N=5 end point t ₀, t ₁, t ₂, t ₃and t ₄convex closure, obtain each bar limit of the minimal convex polygon comprising each end point, be respectively t ₀t ₁, t ₁t ₂, t ₂t ₃, t ₃t ₄and t ₄t ₀; End point t ₀, t ₁, t ₂, t ₃and t ₄abscissa and ordinate be designated as (x respectively ₀, y ₀)=(0.5415756,0.4475305), (x ₁, y ₁)=(0.1177682,0.4999264), (x ₂, y ₂)=(0.2681085,0.3512345), (x ₃, y ₃)=(0.6861621,0.0972497) and (x ₄, y ₄)=(0.9908014,0.3454797), wherein (x ₀, y ₀) be information source terminal point t ₀coordinate.

(2) Delaunay pre-treatment step, comprises following sub-step:

(2.1) for N=5 end point, adopt the method for Delaunay triangulation to obtain 3 Delaunay triangles, be respectively Δ t ₀t ₁t ₂, Δ t ₀t ₂t ₃with Δ t ₀t ₃t ₄;

(2.2) method of the stainer point of calculating 3 end point is adopted, calculate the leg-of-mutton stainer point of each Delaunay, be respectively (0.2702552840,0.3610615245), (0.5029388856,0.3680102729) and (0.7281646053,0.2689202192), by all stainer points of calculating stored in stainer point S set;

(2.3) every two adjacent Delaunay triangles are spliced into a quadrangle, are respectively quadrangle t ₀t ₁t ₂t ₃and t ₀t ₂t ₃t ₄; Adopt the method for the stainer point of calculating 4 end point, obtain the stainer point of each quadrangle, wherein, quadrangle t ₀t ₁t ₂t ₃stainer point be (0.5029388856,0.3680102729), quadrangle t ₀t ₂t ₃t ₄stainer point be (0.5386773638,0.4348096122) and (0.7239365626,0.2630487122); By all stainer points calculated, integrate with in stainer point S set, delete the point (0.5029388856 with same coordinate, 0.3680102729), therefore the stainer point after merging in S set is (0.2702552840,0.3610615245), (0.5029388856,0.3680102729), (0.7281646053,0.2689202192), (0.5386773638,0.4348096122) and (0.7239365626,0.2630487122);

(3) form sub-rectangle step, comprise following sub-step:

(3.1) end point counter k=0 is put; Upgrade the value of XI, XA, YI and YA, be respectively XI=0.5415756, XA=0.5415756, YI=0.4475305, YA=0.4475305;

(3.2) put k=k+1=1, upgrade the value of XI, XA, YI and YA, be respectively XI=0.1177682, XA=0.5415756, YI=0.4475305, YA=0.4999264;

(3.3) put k=k+1=2, upgrade the value of XI, XA, YI and YA, be respectively XI=0.1177682, XA=0.5415756, YI=0.3512345, YA=0.4999264;

(3.4) put k=k+1=3, upgrade XI, XA, YI and YA value, be respectively XI=0.1177682, XA=0.6861621, YI=0.0972497, YA=0.4999264;

(3.5) put k=k+1=4, upgrade the value of XI, XA, YI and YA, be respectively XI=0.1177682, XA=0.9908014, YI=0.0972497, YA=0.4999264;

(3.6) k=k+1=5 is put; Owing to not meeting k≤4, then by end point counter O reset, put k=0; And connection coordinate is (XI, y ₀)=(0.1177682,0.4475305) and (XA, y ₀)=(0.9908014,0.4475305) 2 points, form horizontal line section; Connection coordinate is (x ₀, YI) and=(0.5415756,0.0972497) and (x ₀, YA) and=2 points of (0.5415756,0.4999264), form ordinate section;

(3.7) put k=k+1=1, connection coordinate is (XI, y ₁)=(0.1177682,0.4999264) and (XA, y ₁)=(0.9908014,0.4999264) 2 points, form horizontal line section; Connection coordinate is (x ₁, YI) and=(0.1177682,0.0972497) and (x ₁, YA) and=2 points of (0.1177682,0.4999264), form ordinate section;

(3.8) put k=k+1=2, connection coordinate is (XI, y ₂)=(0.1177682,0.3512345) and (XA, y ₂)=(0.9908014,0.3512345) 2 points, form horizontal line section; Connection coordinate is (x ₂, YI) and=(0.2681085,0.0972497) and (x ₂, YA) and=2 points of (0.2681085,0.4999264), form ordinate section;

(3.9) put k=k+1=3, connection coordinate is (XI, y ₃)=(0.1177682,0.0972497) and (XA, y ₃)=(0.9908014,0.0972497) 2 points, form horizontal line section; Connection coordinate is (x ₃, YI) and=(0.6861621,0.0972497) and (x ₃, YA) and=2 points of (0.6861621,0.4999264), form ordinate section;

(3.10) put k=k+1=4, connection coordinate is (XI, y ₄)=(0.1177682,0.3454797) and (XA, y ₄)=(0.9908014,0.3454797) 2 points, form horizontal line section; Connection coordinate is (x ₄, YI) and=(0.9908014,0.0972497) and (x ₄, YA) and=2 points of (0.9908014,0.4999264), form ordinate section;

(3.11) each horizontal line section and ordinate section form sub-rectangle;

(4) sub-rectangular partition step, comprises following sub-step:

(4.1) each sub-rectangle is all divided into p × p=2 × 2 rectangular grid, obtain the coordinate of each rectangular grid diagonal intersection point, be respectively (0.1553533,0.1593072), (0.1553533,0.2834222), 64 points such as (0.2305234,0.1593072);

(4.2) localization method of point is adopted, obtain be positioned at described convex closure and all rectangular grid diagonal intersection points, be respectively (0.2305234,0.4234565), (0.1553533,0.4868274), (0.2305234,0.4606295) 31 points such as, by they relay points alternatively, stored in relay point set R;

(4.3) complete graph K=(V, E, ω (uv)) is built, node set V=T ∪ S ∪ S ' ∪ R ∪ R ^*, comprise N=|T|=5 end point and M=|S ∪ S ' ∪ R ∪ R ^*| the relay point r of=31+5=36 candidate _4+m, wherein r _4+mcoordinate be (x _4+m, y _4+m), 1≤m≤36; Connect with undirected link uv between any two node u and v in node set V, uv ∈ E; E is the set of all undirected links; The weights ω (uv) of undirected link uv is the Euclidean distance between two node u and v;

(5) ask the frontal planning optimal solution step of balance, comprise following sub-step:

(5.1) based on above-mentioned complete graph K, the front linear programming model based on information flow of balance is built; Comprise target function and constraints;

(5.1.1) target function is wherein, directed link set decision variable is directed link in complete graph K total information transmission rate decision variable coefficient

(5.1.2) constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition:

Information flow conservation condition:

Information flow upper bound condition:

Non-negative condition:

Wherein, 1≤i≤4; U, v, t ₀, t _i∈ V, v _←u () refers to that beginning node is the set of all directed link terminal notes of u, V _→u () represents that terminal note is the set of all directed link beginning nodes of u; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; for directed link on total information transmission rate, it equals directed link upper all maximum; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; H is the total information transmission rate that information source sends, and puts h and is normalized to 1;

(5.2) utilize linear programming method to ask the front optimal solution based on the linear programming model of information flow of described balance, export the front target function value C based on the linear programming model of information flow of described balance _p=1.209665387; Export each directed link the rate of information throughput non-zero values is respectively with export each directed link total information transmission rate non-zero values is respectively with export the total information transmission rate f (uv) of each undirected link uv, non-zero values is respectively f (t ₀r ₃₆)=f (r ₃₆t ₁)=f (r ₃₆t ₂)=1 and f (t ₀r ₃₈)=f (r ₃₈t ₃)=f (r ₃₈t ₄)=1;

(5.3) target function value C _pmeet C _p<CI, minimum cost value CI=C before horizontalization weighing apparatus _p=1.209665387, enter sub-step (5.4);

(5.4) because the total information transmission rate of the undirected link of all of its neighbor of all relay points is not zero entirely, therefore be not the relay point of zero entirely for the total information transmission rate of the adjacent undirected link of relay point, do not meet more than 2 relay points on a line segment, enter sub-step (5.5);

(5.5) the total information transmission rate of searching the undirected link of its all of its neighbor is not the relay point of zero entirely, and by these relay points stored in current optimum relay point set R ^*, comprise (0.2702552840,0.3610615245) and (0.7281646053,0.2689202192), its size is M ^*, be designated as M ^*=| R ^*|=2, enter step (6);

(6) relay point is adjusted to equilbrium position step, to R ^*two points finely tune; Comprise following sub-step:

(6.1) counter RD=1 is put back;

(6.3) vectorial addition is adopted to calculate relay point r ₅making a concerted effort of (its coordinate being (0.2702552840,0.3610615245)) wherein, for the adjacent directed link in edge the power in direction, size

(6.4) meet put BL=BL+1=1, enter sub-step (6.5); Wherein, for relay point r ₅make a concerted effort size, get with joint efforts error ε ₁=0.0001;

(6.5) put j=j+1=2, meet j≤M*=2, adopt vectorial addition to calculate relay point r ₆making a concerted effort of (its coordinate being (0.7281646053,0.2689202192)) wherein, for the adjacent directed link in edge the power in direction, size

(6.6) meet put BL=BL+1=2, enter sub-step (6.7); Wherein, for relay point r ₆make a concerted effort size;

(6.7) put j=j+1=3, do not meet j≤M ^*=2, but meet BL=M ^*=2, show that all relay points adjust to equilbrium position, by current optimum set of relay nodes R ^*be updated to all relay points adjusting to equilbrium position, be respectively (0.2702552840,0.3610615245) and (0.7281646053,0.2689202192), enter step (7);

(7) ask the rear Optimal Solution of Linear Programming step of balance, comprise following sub-step:

(7.1) the rear complete graph K of balance is built ^*=(V ^*, E ^*, ω ^*(u ' v ')); Node set V ^*=T ∪ R ^*, comprise N=5 end point and M ^*=2 relay points adjusted to behind equilbrium position;

(7.2) based on complete graph K after above-mentioned balance ^*, based on the linear programming model of information flow after building balance: comprise target function and constraints;

(7.2.1) target function is wherein, directed link set decision variable is complete graph K ^*middle directed link total information transmission rate decision variable coefficient

(7.2.2) constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition:

Information flow conservation condition:

Information flow upper bound condition:

Non-negative condition:

Wherein, 1≤i≤4; U ', v ', t ₀, t _i∈ V ^*, represent that beginning node is the set of all directed link terminal notes of u ', represent that terminal note is the set of all directed link beginning nodes of u '; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; for directed link on total information transmission rate, equal directed link upper all maximum; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; H is the total information transmission rate that information source sends, and puts h and is normalized to 1;

(7.3) utilize linear programming method to ask optimal solution based on the linear programming model of information flow after described balance, export the target function value based on the linear programming model of information flow after described balance export each directed link the rate of information throughput non-zero values is respectively with export each directed link total information transmission rate non-zero values is respectively with

(7.4) owing to balancing rear target function value meet minimum cost value after horizontalization weighing apparatus

{CI}^{*} = C_{p}^{*} = 1.209665387,

Rotor step (7.5);

(7.5) owing to meeting 0≤CI-CI ^*≤ ε ₂, enter sub-step (7.6);

(7.6) owing to not meeting 0≤CL ^*-CI ^*≤ ε ₃, minimum cost value CL*=CI*=1.209665387 and put p=p+1=3 after putting last round of balance, enters step (8) and again divides; Wherein, the first cost error ε ₂get 0.00001, the second cost error ε ₃get 0.00001;

(8) again divide, comprise following sub-step:

(8.1) be p × p=3 × 3 rectangular grid by every sub-rectangular partition in constraint rectangle, calculate the coordinate of each rectangular grid diagonal intersection point, for (0.1428249,0.1386214), (0.1428249,0.2213647), 144 points such as (0.1428249,0.3041080);

(8.2) localization method of point is adopted, find be positioned at described convex closure and all rectangular grid diagonal intersection points, for (0.1929383,0.4314812), (0.2430518,0.3993825), (0.2430518,0.4314812) 73 points such as, by these intersection points relay point alternatively, stored in relay point set R;

(8.3) complete graph K=(V, E, ω (uv)) is built, node set V=T ∪ S ∪ S ' ∪ R ∪ R ^*, comprise N=|T|=5 end point and M=|S ∪ S ' ∪ R ∪ R ^*| the relay point r of=73+5=78 candidate _4+m, wherein r _4+mcoordinate be (x _4+m, y _4+m), 1≤m≤78;

(9) again ask the frontal planning optimal solution of balance, comprise following sub-step:

(9.1) based on the complete graph K that step (8.3) obtains, the front linear programming model based on information flow of balance is built;

(9.2) utilize linear programming method to ask the front optimal solution based on the linear programming model of information flow of described balance, export the front target function value C based on the linear programming model of information flow of described balance _p=1.209665387; Export each directed link the rate of information throughput non-zero values is respectively with export each directed link total information transmission rate non-zero values is respectively with export the total information transmission rate f (uv) of each undirected link uv, non-zero values is respectively f (t ₀r ₇₈)=f (r ₇₈t ₁)=f (r ₇₈t ₂)=1 and f (t ₀r ₈₀)=f (r ₈₀t ₃)=f (r ₈₀t ₄)=1;

(9.3) owing to balancing front target function value C _pmeet C _p<CI, minimum cost value CI=C before horizontalization weighing apparatus _p=1.209665387, because the total information transmission rate of the undirected link of all of its neighbor not meeting all relay points is zero entirely, enter (9.4);

(9.4) for the total information transmission rate of the adjacent undirected link of relay point be not entirely zero relay point, on a line segment, enter sub-step (9.5) owing to not meeting wherein more than 2 relay points;

(9.5) relay point that the total information transmission rate meeting the undirected link of its all of its neighbor is not zero is entirely searched, and by these relay points stored in current optimum relay point set R ^*, comprise (0.2702552840,0.3610615245) and (0.7281646053,0.2689202192), its size is M ^*, be designated as M ^*=| R ^*|=2, enter step (10);

(10) again adjust relay point to equilbrium position, comprise following sub-step:

(10.1) counter RD=1 is put back; Put relay point variable j=1, horizontalization weighing apparatus counter BL=0;

(10.2) vectorial addition is adopted to obtain current optimum relay point set R ^*in relay point r ₅making a concerted effort of (its coordinate being (0.2702552840,0.3610615245)) wherein, for the adjacent directed link in edge the power in direction, size

(10.3) owing to meeting put BL=BL+1=1, put j=j+1=2; Owing to meeting j≤M ^*=2, adopt vectorial addition to calculate current optimum relay point set R ^*in relay point r ₆making a concerted effort of (its coordinate being (0.7281646053,0.2689202192)) wherein, for the adjacent directed link in edge the power in direction, size wherein, for relay point r ₅make a concerted effort size, get with joint efforts error ε ₁=0.00001;

(10.4) owing to meeting put BL=BL+1=2, put j=j+1=3; Owing to not meeting j≤M ^*=2, enter sub-step (10.5); Wherein, for relay point r ₆make a concerted effort size;

(10.5) owing to meeting BL=M ^*=2, show that all relay points adjust to equilbrium position, by current optimum set of relay nodes R ^*be updated to all relay points adjusting to equilbrium position, be respectively (0.2702552840,0.3610615245) and (0.7281646053,0.2689202192), enter step (11);

(11) again ask the rear Optimal Solution of Linear Programming of balance, comprise following sub-step:

(11.1) complete graph K is built ^*=(V ^*, E ^*, ω ^*(u ' v ')), node set V ^*=T ∪ R ^*, comprise N=5 end point and M ^*=2 relay points adjusted to behind equilbrium position;

(11.2) based on the complete graph K that (11.1) obtain ^*, build the linear programming model based on information flow after balancing:

(11.3) utilize linear programming method to ask optimal solution based on the linear programming model of information flow after described balance, export the target function value based on the linear programming model of information flow after described balance export each directed link the rate of information throughput non-zero values is respectively with export each directed link total information transmission rate non-zero values is respectively with

(11.4) owing to balancing rear target function value meet minimum cost value after horizontalization weighing apparatus

{CI}^{*} = C_{p}^{*} = 1.209665387,

Enter sub-step (11.5);

(11.5) owing to meeting 0≤CI-CI ^*≤ ε ₂, enter sub-step (11.6);

(11.6) owing to meeting 0≤CL ^*-CI ^*≤ ε ₃, enter step (12); Wherein, the first cost error ε ₂=0.00001; Second cost error ε ₃=0.00001;

(12) again carry out Delaunay reprocessing, comprise following sub-step:

(12.1) end point counter k=0 is put; Search with end point t ₀for all angles that any two links of public vertex are formed, i.e. ∠ r ₅t ₀r ₆;

(12.2) owing to meeting angle ∠ r ₅t ₀r ₆be less than 120 °, therefore adopt the method for the stainer point of calculating 3 end point, obtain the stainer point on three summits forming above-mentioned angle, namely (0.5407003445,0.4437396571), all stored in supplement stainer point S set ' in, enter sub-step (12.4);

(12.4) owing to not meeting k=N-1=4, k=k+1=1 is put; Owing to not existing with end point t ₁for all angles that any two links of public vertex are formed, do not meet the condition that angle is less than 120 °, enter step (12.5);

(12.5) owing to not meeting k=N-1=4, k=k+1=2 is put; Owing to not existing with end point t ₂for all angles that any two links of public vertex are formed, do not meet angle and be less than 120 °, enter sub-step (12.6);

(12.6) owing to not meeting k=N-1=4, k=k+1=3 is put; Owing to not existing with end point t ₃for all angles that any two links of public vertex are formed, do not meet angle and be less than 120 °, enter sub-step (12.7);

(12.7) owing to not meeting k=N-1=4, k=k+1=4 is put; Owing to not existing with end point t ₄for all angles that any two links of public vertex are formed, do not meet angle and be less than 120 °, enter sub-step (12.8);

(12.8) owing to meeting k=N-1=4, but do not meet S ' for empty set, enter step (13), again carry out sub-rectangular partition;

(13) again carry out sub-rectangular partition, comprise following sub-step:

(13.1) be p × p=3 × 3 rectangular grid by every sub-rectangular partition, obtain the coordinate of each rectangular grid diagonal intersection point, for (0.1428249,0.1386214), (0.1428249,0.2213647), 144 points such as (0.1428249,0.3041080);

(13.2) localization method of point is adopted, obtain be positioned at described convex closure and all rectangular grid diagonal intersection points, for (0.1929383,0.4314812), (0.2430518,0.3993825), (0.2430518,0.4314812) 73 points such as, by these relay points alternatively, stored in relay point set R;

(13.3) complete graph K=(V, E, ω (uv)) is built, node set V=T ∪ S ∪ S ' ∪ R ∪ R ^*, comprise N=|T|=5 end point and M=|S ∪ S ' ∪ R ∪ R ^*| the relay point r of=73+5+1=79 candidate _4+m, wherein r _4+mcoordinate be (x _4+m, y _4+m), 1≤m≤79; Enter step (14);

(14) again ask the frontal planning optimal solution of balance, comprise following sub-step:

(14.1) based on the complete graph K that complete graph step (13.3) obtains, the front linear programming model based on information flow of balance is built;

(14.2) utilize linear programming method to ask the front optimal solution based on the linear programming model of information flow of described balance, export the front target function value C based on the linear programming model of information flow of described balance _p=1.209623475; Export each directed link the rate of information throughput non-zero values is respectively with export each directed link total information transmission rate non-zero values is respectively with export the total information transmission rate f (uv) of each undirected link uv, non-zero values is respectively f (t ₀r ₈₃)=f (r ₈₃r ₇₈)=f (r ₇₈t ₁)=f (r ₇₈t ₂)=1 and f (r ₈₃r ₇₉)=f (r ₇₉t ₃)=f (r ₇₉t ₄)=1;

(14.3) owing to balancing front target function value C _pmeet C _p<CI, minimum cost value CI=C before horizontalization weighing apparatus _p=1.209623475, enter sub-step (14.4);

(14.4) the total information transmission rate of the undirected link of all of its neighbor owing to not meeting all relay points is zero entirely; Total information transmission rate for the adjacent undirected link of relay point is not the relay point of zero entirely, on a line segment, enters sub-step (14.5) owing to not meeting wherein more than 2 relay points;

(14.5) relay point that the total information transmission rate meeting the undirected link of its all of its neighbor is not zero is entirely searched, and by these relay points stored in current optimum relay point set R ^*, comprise (0.2702552840,0.3610615245), (0.7281646053,0.2689202192) and (0.5407003445,0.4437396571), its size is M ^*=| R ^*|=3, enter step (15), adjust relay point further;

(15) adjustment relay point, to equilbrium position, comprises following sub-step further:

(15.1) counter RD=1 is put back; Put relay point variable j=1, horizontalization weighing apparatus counter BL=0; Vectorial addition is adopted to calculate current optimum relay point set R ^*in relay point r ₅making a concerted effort of (its coordinate being (0.2702552840,0.3610615245)) wherein, for the adjacent directed link in edge the power in direction, size

(15.2) owing to not meeting by relay point r ₅it is made a concerted effort displacement Δ=1/, direction (2 × RD+3)=0.2, put enter sub-step (15.3) again; Wherein, for relay point r ₅make a concerted effort size, make a concerted effort error ε ₁=0.00001;

(15.3) put j=j+1=2, meet j≤M ^*=3, adopt vectorial addition to calculate current optimum relay point set R ^*in relay point r ₆making a concerted effort of (its coordinate being (0.7281646053,0.2689202192)) wherein, for the adjacent directed link in edge the power in direction, size

(15.4) owing to not meeting by relay point r ₆it is made a concerted effort displacement Δ=1/, direction (2 × RD+3)=0.2, put enter sub-step (15.5) again; Wherein, for relay point r ₆make a concerted effort size;

(15.5) put j=j+1=3, meet j≤M ^*=3, adopt vectorial addition to calculate current optimum relay point set R ^*in relay point r ₇making a concerted effort of (its coordinate being (0.5407003445,0.4437396571)) wherein, for the adjacent directed link in edge the power in direction, size

(15.6) owing to not meeting by relay point r ₇it is made a concerted effort displacement Δ=1/, direction (2 × RD+3)=0.2, put enter sub-step (15.7) again; Wherein, for relay point r ₇make a concerted effort size;

(15.7) put j=j+1=4, do not meet j≤M ^*=3; And do not meet BL=M ^*=3; Put RD=RD+1, enter sub-step (15.1); Multiple exercise sub-step (15.1) ~ (16.6), relay point r ₅, r ₆and r ₇move to new position respectively, coordinate be updated to respectively (0.2695887762,0.3575665531), (0.7254109975,0.2651414093) and (0.5396563548,0.4393207063); Enter step (16), ask the rear Optimal Solution of Linear Programming of balance further;

(16) ask the rear Optimal Solution of Linear Programming of balance, comprise following sub-step:

(16.1) the rear complete graph K of balance is built ^*=(V ^*, E ^*, ω ^*(u ' v ')), node set V ^*=T ∪ R ^*, comprise N=5 end point and M ^*adjust to the relay point behind equilbrium position for=3 to form;

(16.2) complete graph K after the balance obtained based on (16.2) ^*, build the linear programming model based on information flow after balancing:

(16.3) utilize linear programming method to ask optimal solution based on the linear programming model of information flow after described balance, export the target function value based on the linear programming model of information flow after described balance export each directed link the rate of information throughput non-zero values is respectively with export each directed link total information transmission rate non-zero values is respectively with

(16.4) owing to balancing rear target function value meet minimum cost value after horizontalization weighing apparatus

{CI}^{*} = C_{p}^{*} = 1.209574564,

Enter sub-step (16.5);

(16.5) owing to not meeting 0≤CI-CI ^*≤ ε ₂, put p=p+1=4, enter step (4);

Perform step (4) ~ step (7), obtain the frontal planning optimal solution CI=1.209574564 of balance; Minimum cost value CI after balance ^*=1.209574564;

(16.6) owing to meeting 0≤CL ^*-CI ^*≤ ε ₃, enter step (17);

(17) carry out Delaunay reprocessing, the S ' of acquisition is empty set, shows to find the Internet Transmission mode with minimum cost, exports CI ^*=1.209574564; Export all nonzero information transmission rates numerical value, be respectively with export all non-zero total information transmission rates numerical value, be respectively with export current optimum relay point set R ^*in relay point coordinate, be respectively (0.2695887762,0.3575665531), (0.7254109975,0.2651414093) and (0.5396563548,0.4393207063); Adopt the result of the network transfer method acquisition of embodiment as shown in Figure 9.

There is relay point and uneven (the relay point r of end point density distribution in this embodiment ₅from end point t ₂very near, relay point r ₇from end point t ₀very near), if only adopt the spatial network coding method based on non-homogeneous division in prior art, need to adopt larger division parameter p just can obtain the relay point of effective candidate, but when p increases, amount of calculation when asking Optimal Solution of Linear Programming is by with the increase of the biquadratic form of p.Owing to adopting the method for Delaunay preliminary treatment and reprocessing in the inventive method, make to find optimal solution fast when dividing p and being less, as can be seen here, the present invention effectively reduces amount of calculation, accelerates convergence rate, thus effectively promotes network transmission performance.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims

1. the network transfer method adopting the spatial network based on Delaunay triangulation to encode, is characterized in that, comprise the steps:

(1) convex closure of N number of end point is obtained; N is positive integer;

(2) for N number of end point, the method of Delaunay triangulation is adopted to obtain (2N-5) individual Delaunay triangle at the most, obtain all Delaunay leg-of-mutton stainer point and all two adjacent Delaunay triangles form the stainer point of quadrangle, stored in stainer point S set;

(3) obtain horizontal line section and ordinate section respectively according to the horizontal stroke of each end point, ordinate, and obtain sub-rectangle according to each horizontal line section and ordinate section;

(4) be p × p rectangular grid by each sub-rectangular partition, obtain the coordinate of each rectangular grid diagonal intersection point; Obtain all diagonal intersection points be positioned at convex closure on convex closure, and relay point alternatively, stored in relay point set R; To end point set T, stainer point S set, relay point set R, supplement stainer point S set ' and current optimum relay point set R ^*union build complete graph; P gets the positive integer being not less than 2;

(5) build the front linear programming model based on information flow of balance based on described complete graph, its target function is its constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition; Utilize linear programming method to obtain the frontal planning optimal solution of balance, export the target function value C before balance _p, each directed link the rate of information throughput with total information transmission rate numerical value, and balance before minimum cost value CI;

Current optimum relay point set is formed by the relay point of " the total information transmission rate of the undirected link of its all of its neighbor is not zero entirely "; Wherein, i is destination end point counter, 1≤i≤N-1;

(6) vectorial addition is adopted to obtain making a concerted effort of each relay point in current optimum relay point set; The position of each relay point is moved to equilbrium position along its resultant direction, until the making a concerted effort at the error ε that makes a concerted effort of relay point after mobile ₁in scope;

(7) the rear complete graph of balance is built to the relay point after end point, movement; Based on the linear programming model based on information flow after complete graph structure balance after described balance, its target function is its constraints comprises information flow conservation condition, information flow upper bound condition and non-negative condition; Utilize linear programming method to obtain the rear Optimal Solution of Linear Programming of balance, export the target function value after balance each directed link the rate of information throughput with total information transmission rate numerical value, and balance after minimum cost value CI ^*;

Judge whether to meet if so, then by the target function value after described balance as minimum cost value CI after balance ^*;

If so, satisfied 0≤CL is then judged whether ^*-CI ^*≤ ε ₃, if so, enter step (8); If not, then minimum cost value CI after balancing ^*as minimum cost value CL after last round of balance ^*, juxtaposition p=p+1, enters step (4);

(8) search with end point t _kfor all angles that any two links of public vertex are formed; Adopt the method for the stainer point of calculating 3 end point, obtain the stainer point that the angle formed is less than three summits of 120 °, stored in supplement stainer point S set '; Wherein, k is end point counter; 0≤k≤N-1;

Judge supplement stainer point S set ' whether be empty set, if not, enter step (4); If so, the rear each directed link of balance is then exported the rate of information throughput value and total information transmission rate value, balance after minimum cost value CI ^*, and current optimum relay point set R ^*in relay point coordinate;

Wherein, refer to the front directed link of balance weights; A refers to the front directed link set of balance; refer to the rear directed link of balance weights; A ^*refer to the rear directed link set of balance; ε ₂refer to the first cost error, ε ₃refer to the second cost error.

2. network transfer method as claimed in claim 1, it is characterized in that, described step (2) specifically comprises following sub-step:

(2.2) adopt the method for the stainer point of calculating 3 end point, obtain the leg-of-mutton stainer point of each Delaunay;

(2.3) every two adjacent Delaunay triangles are spliced into a quadrangle, adopt the method for the stainer point of calculating 4 end point to obtain the stainer point of each quadrangle; By all stainer points of obtaining stored in stainer point S set.

3. network transfer method as claimed in claim 1, it is characterized in that, described step (3) specifically comprises following sub-step:

(3.1) end point counter k=0 is put;

(3.3) upgrade minimum abscissa value XI, maximum abscissa value XA, the minimum ordinate value YI and maximum ordinate value YA of end point, comprise following process:

(3.3.4) judge whether to meet YA<y _k, be put YA=y _k, then rotor step (3.4); Otherwise directly enter sub-step (3.4);

(3.4) put k=k+1, and be back to step (3.2);

(3.5) empty end point counter, put k=0;

(3.7) connection coordinate is (XI, y _k) and (XA, y _k) 2 points, form horizontal line section; Connection coordinate is (x _k, YI) and (x _k, YA) 2 points, form ordinate section, enter sub-step (3.8);

(3.8) put k=k+1, enter sub-step (3.6);

(3.9) each horizontal line section and ordinate section form sub-rectangle; Wherein, (x _k, y _k) be end point t _kcoordinate.

4. network transfer method as claimed in claim 1, it is characterized in that, step (4) comprises following sub-step:

(4.1) be p × p rectangular grid by each sub-rectangular partition, obtain the coordinate of each rectangular grid diagonal intersection point;

(4.2) adopt the localization method of point, obtain and be positioned on convex closure and the rectangular grid diagonal intersection point of convex closure, by described intersection point relay point alternatively, stored in relay point set R;

Wherein, connect with undirected link uv between any two node u and v in node set V, uv ∈ E, E refer to the set of all undirected links; The weights ω (uv) of undirected link uv is the Euclidean distance between two node u and v; T refers to the end point set be made up of N number of end point; S refers to the set of stainer point; S ' refers to the set of supplement stainer point; R refers to relay point set; R ^*refer to current optimum relay point set.

5. network transfer method as claimed in claim 4, it is characterized in that, described step (5) specifically comprises following sub-step:

(5.1) based on described complete graph K, build the front linear programming model based on information flow of balance, comprise target function and constraints;

Target function is wherein, directed link set decision variable is directed link in complete graph K total information transmission rate decision variable coefficient

Information flow conservation condition:

Information flow upper bound condition:

Non-negative condition:

(5.2) utilize linear programming method to obtain the front optimal solution based on the linear programming model of information flow of described balance, export the front target function value C based on the linear programming model of information flow of described balance _p; Export each directed link the rate of information throughput value and total information transmission rate value and the value of total information transmission rate f (uv) of each undirected link uv; Wherein,

Wherein, 1≤i≤N-1; U, v, t ₀, t _i∈ V, v _←u () represents that beginning node is the set of all directed link terminal notes of u, V _→u () represents that terminal note is the set of all directed link beginning nodes of u; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; for directed link on total information transmission rate, it equals directed link upper all maximum; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; H is the total information transmission rate that information source sends, h>0.

6. network transfer method as claimed in claim 5, it is characterized in that, described step (6) specifically comprises following sub-step:

(6.1) counter RD=1 is put back;

(6.3) vectorial addition is adopted to obtain relay point r _n-1+jmake a concerted effort wherein, for the adjacent directed link in edge the power in direction, size

(6.6) judge whether to meet BL=M ^*, if so, then by current optimum set of relay nodes R ^*be updated to all relay points adjusting to equilbrium position, enter step (7); If not, then put RD=RD+1, enter sub-step (6.2).

7. network transfer method as claimed in claim 4, it is characterized in that, described step (7) specifically comprises following sub-step:

Information flow conservation condition:

Information flow upper bound condition:

Non-negative condition:

(7.3) based on the optimal solution of the linear programming model of information flow after utilizing linear programming method acquisition to balance, the target function value based on the linear programming model of information flow after balancing is exported export each directed link the rate of information throughput with total information transmission rate value;

Wherein, E ^*refer to the set of all undirected links; The weights ω of undirected link u ' v ' ^*(u ' v ') is the Euclidean distance between two node u ' and v ';

Wherein, 1≤i≤N-1; U ', v ', t ₀, t _i∈ V ^*, represent that beginning node is the set of all directed link terminal notes of u ', represent that terminal note is the set of all directed link beginning nodes of u '; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; for directed link on total information transmission rate, equal directed link upper all maximum; represent from information source terminal point t ₀be sent to destination end point t _iinformation flow in directed link on the rate of information throughput; H is the total information transmission rate that information source sends, h>0; ε ₂be the first cost error, ε ₃it is the second cost error.

8. network transfer method as claimed in claim 1, it is characterized in that, described step (8) specifically comprises following sub-step:

(8.1) end point counter k=0 is put;

(8.5) judge whether S ' is empty set; If so, then CI is exported ^*, all nonzero information transmission rates value and non-zero total information transmission rate value, and export current optimum relay point set R ^*in relay point coordinate; If not, then step (4) is entered.

9. network transfer method as claimed in claim 1, is characterized in that, the described error ε that makes a concerted effort ₁meet 0≤ε ₁≤ 0.0001.

10. network transfer method as claimed in claim 7, it is characterized in that, described first cost error meets 0≤ε ₂≤ 0.0001; Described second cost error ε ₃meet 0≤ε ₃≤ 0.0001.