CN108683593B - K short path calculation method - Google Patents
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- CN108683593B CN108683593B CN201810752666.0A CN201810752666A CN108683593B CN 108683593 B CN108683593 B CN 108683593B CN 201810752666 A CN201810752666 A CN 201810752666A CN 108683593 B CN108683593 B CN 108683593B
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L45/00—Routing or path finding of packets in data switching networks
- H04L45/12—Shortest path evaluation
- H04L45/123—Evaluation of link metrics
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L45/00—Routing or path finding of packets in data switching networks
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- H04L45/124—Shortest path evaluation using a combination of metrics
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Abstract
The invention discloses a K short path calculation method, and relates to the technical field of communication. Respectively acquiring paths from a source node to each neighbor node and adding an extended path set; and according to the sequence of the weights of the paths in the extended path set from high to low, taking out one path each time and expanding the path according to the breadth of the network topology, adding the non-K short path obtained by expansion into the extended path set, continuing to expand, adding the K short path obtained by expansion into the shortest path set, and outputting the shortest path set in sequence. The invention can ensure that all K short paths meeting the conditions are found, and meanwhile, the convergence speed of path calculation according to the weight of the path is higher, thereby quickly obtaining the calculation result.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a K short path calculation method.
Background
The Shortest Path Problem (Shortest Path promlem) is one of the most basic problems in the network optimization Problem. The basic description of the problem is: in a given network, a shortest (distance, delay, cost) path between a source node and a sink node is found. The K short Path Problem (K-short Path promlem) is based on the Shortest Path Problem, i.e. the first K Shortest paths between a source node and a sink node are found from a given network. The two problems are widely applied to a plurality of scenes such as travel route planning, logistics transportation planning, urban rail transit planning, communication network planning, satellite network data transmission and the like. At present, the shortest path planning algorithm comprises a Dijkstra algorithm, a Floyd algorithm, an A-Star algorithm, a Bellman-Ford algorithm, various intelligent algorithms (a neural network algorithm, an ant colony algorithm, a genetic algorithm, a simulated annealing algorithm) and the like, and the algorithms usually do not consider the constraint conditions of nodes, paths, forbidden nodes, forbidden paths and the like, so that the method cannot be applied to the actual scene with the constraint conditions.
The existing K short path solving method is that a minimum spanning tree is obtained by utilizing a full-network topology, nodes or links which are necessary to pass in a path to be built are sequenced on the minimum spanning tree obtained through calculation, segmented calculation is carried out according to the sequenced nodes or links which are necessary to pass, and paths obtained through segmented calculation are spliced to obtain the K short path.
The other K short path solving method is combined with the shortest path method and considers the constraint conditions of the must-pass node, the must-pass link, the forbidden node, the forbidden path and the like to obtain the K short path. Taking the 3 × 3 network shown in fig. 1 as an example for explanation, when the shortest path from node 5 to node 3 and including node 7 is calculated, first K shortest paths obtained based on the shortest path algorithm are first obtained, and then whether constraint conditions are met is determined one by one, where the first K shortest paths are:
(1)5-6-3；
(2)5-2-3；
(3)5-8-9-6-3；
(4)5-4-1-2-3；
(5)5-8-7-4-1-2-3；
(6)5-4-7-8-9-6-3。
because the nodes and/or links are bound to pass through in the reverse direction of the shortest path, when the shortest path method is used, the first 4 shortest paths are calculated to obtain a path (5) meeting the condition, and then a plurality of paths are possibly spanned to obtain a second path (6) meeting the condition. Therefore, under the constraint condition, a path meeting the condition can only be obtained by using the shortest path method to calculate the first K-1 shortest paths, so that it takes time to obtain all the K short paths meeting the constraint condition, and when the value of K is too small, the path meeting the condition cannot be obtained.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a K short path calculation method, which can ensure that all K short paths meeting the conditions are found, and meanwhile, the convergence speed of path calculation according to the weight of the paths is higher, so that the calculation result is obtained quickly.
The invention provides a K short path calculation method, which comprises the following steps:
respectively acquiring paths from a source node to each neighbor node and adding an extended path set;
and according to the sequence of the weights of the paths in the extended path set from high to low, taking out one path each time and expanding the path according to the breadth of the network topology, adding the non-K short path obtained by expansion into the extended path set, continuing to expand, adding the K short path obtained by expansion into the shortest path set, and outputting the shortest path set in sequence.
On the basis of the technical scheme, the weight of the path comprises the criticality, and the numerical value of the criticality is the number of the constraint conditions met by the path.
On the basis of the above technical solution, when the criticality values of the plurality of paths are the same, the weight of the path further includes at least one of a distance, a hop count, and a delay of the path, or any combination thereof.
On the basis of the technical scheme, the path taken out each time is one path meeting the most constraint conditions or one of all paths meeting the same number of constraint conditions.
On the basis of the technical scheme, the extended path set is a binary heap, and paths with high weight are stored at the head of the binary heap.
On the basis of the technical scheme, when one path is taken out each time, if the path forms a ring, the path is discarded.
On the basis of the technical scheme, the method further comprises the following steps: repeating the expanding operation of the paths in the expanded path set until the total number of the paths in the shortest path set is K, or all the paths in the expanded path set are taken out.
On the basis of the technical scheme, the method further comprises the following steps: when the operation on the extended path set reaches an operation upper limit value, stopping calculation, and sequencing and outputting all paths in the shortest path set;
the operation on the expansion path set comprises a taking path, a joining path and a deleting path.
On the basis of the technical scheme, the method further comprises the following steps: and when the total number of the paths in the extended path set reaches the path upper limit value, stopping calculation, and sequencing all the paths in the shortest path set and outputting the sequenced paths.
On the basis of the above technical solution, the method for sorting all paths in the shortest path set includes: according to at least one of distance, hop count and delay of the path, or any combination thereof.
Compared with the prior art, the invention has the following advantages:
(1) the method gradually expands from the source node to the destination node according to the breadth of the network topology, can ensure that all K short paths meeting the conditions are found, and meanwhile, the convergence speed of path calculation according to the weight of the paths is high, so that the calculation result is obtained quickly.
(2) The calculation process is controlled by setting the upper limit value of the operation times or the total number of the paths of the extended path set, and a part of or even all K short paths can be quickly obtained under the condition that the calculation resources (memory) and the calculation time are limited.
(3) When the extracted path is expanded, the adjacent node of the tail end node of the extracted path can be expanded each time, an expansion method can be flexibly set according to the actual situation, in addition, the constraint condition can be a necessary node/path, a forbidden node/path and the like, and the requirements of various application scenes are met.
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FIG. 1 is a schematic diagram of a 3 × 3 node network topology;
fig. 2 is a schematic diagram of a network topology of a 4 × 4 node according to a first embodiment of the present invention;
FIG. 3 is a flowchart of a method for calculating K short paths according to a first embodiment of the present invention;
fig. 4 shows a short path obtained by the K short path calculation method according to the first embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The invention provides a K short path calculation method, which comprises the following steps:
and respectively acquiring the path from the source node to each neighbor node and adding the path into the extended path set.
And according to the order of the weights of the paths in the extended path set from high to low, taking out one path each time and extending according to the breadth of the network topology, adding the non-K short paths obtained by extension into the extended path set, continuing to extend, adding the K short paths obtained by extension into the shortest path set, and outputting the shortest paths in sequence.
The constraint condition may be a must-pass node, a must-pass link, a forbidden node, a forbidden path, etc., without limitation. The constraint condition that the K short path should satisfy is at least one, and may also be multiple, for example, constraint condition 1 that the K short path satisfies is a must-pass node, and constraint condition 2 that the K short path satisfies is a must-pass link.
When the extension is performed from the source node to the sink node in a plurality of times, the extended path does not satisfy the paths of all the constraints, or, although all the constraints are satisfied, the extended path does not reach the sink node, and the extended path is a non-K short path.
For the sake of clarity of the method embodiments, the following definitions are first given:
undirected networks are represented by graph G (V, E), where V ═ V i1,2, …, n, representing a node set, E ═ E { (E) }j| i ═ 1,2, …, m } denotes the set of links in the network, ej＝(vi,vi+1) Denotes the starting node as viAnd the end node is vi+1The link of (2). | V | represents the total number of nodes in undirected network graph G, | E | represents the total number of edges in graph G.
Must pass resource set I ═ vi|vi∈V/{vs,vd},ejE, and I represents the total number of the specified resources in the must-be-passed resource set. P (v)s,vd) Representing a node vsTo node vdThe weight of the path comprises the criticality, the numerical value of the criticality is the number of the constraint conditions met by the path, and the criticality of the path is defined as key (P (v)s,vi) Represents a path P (v)s,vd) The greater the criticality is, the more the specified resources are included in the path. When key (P (v)s,vd) If | I |), it means that the path includes all the specified resources.
According to the above definition, the K short path problem can be described as: in no at allInto the network G (V, E), a starting node V is givensDestination node vdAnd must pass through resource set I, compute from vsTo vdThe least costly K simple loop-free paths that contain the must-go resource set I.
The extended path set is represented by a container U for storing data from a source node vsTo an arbitrary node viSimple loop-free path P (v)s,vi) Each path has a weight, which includes criticality. The container U has the functions of inserting path, deleting path and sorting according to a certain plan, and the maximum capacity of the container U is recorded as MmaxThe current volume of the container U is marked as Mcur. The maximum number of operable (i.e. delete or insert operations) of a container U is denoted CmaxAnd the current operation times of the container is recorded as Ccur. The shortest path set is represented by a container T and used for storing the shortest paths which meet the conditions, and the number of the shortest paths which meet the must-pass resource set I and are obtained through calculation is recorded as k.
A first embodiment of the present invention provides a method for calculating a K-short path, which considers that multiple types of constraints are simultaneously satisfied, for example, a must-pass node and a must-pass link, all must-pass nodes and must-pass links form a must-pass resource set, and a weight of a path includes a number of paths satisfying the constraints. In this application, a path is synonymous with a link.
The K short path calculation method comprises the following steps: and if the link or the node on the link is in the necessary resource set and the weight of the path is updated, the path with the highest weight is preferentially taken for expansion next time or one of all paths meeting the same number of constraint conditions. And expanding outwards layer by layer from the source node of the path, adding the K short paths obtained by expansion into the shortest path set, and repeating the expansion operation on the paths in the expanded path set until the total number of the paths in the shortest path set is K, or taking out all the paths in the expanded path set.
Specifically, the extended path set is a binary heap, and the paths with high weights are stored at the head of the binary heap. Each time a path is taken, if the path is looped, it is discarded.
The weight of a path includes criticality, the value of which is the number of constraints that the path satisfies.
As shown in FIG. 2, given a network topology of 4 x 4 network nodes, a slave v is computed1To v16Comprises a link (v)3,v7) And node v10K minimum hop count paths.
The calculation method of this embodiment uses a binary heap as a container U for storing extended paths, the binary heap uses the criticality of the paths as a sorting principle, the paths with larger criticality values are preferentially placed at the head of the heap, and the paths are preferentially taken out when elements in the heap are taken out, for example, the maximum capacity of the binary heap is set to 10000, the number of operations of the binary heap is set to 10000, and the found shortest path satisfying the condition is stored by another binary heap.
Referring to fig. 3, the method for calculating the K short path in this embodiment specifically includes the following steps:
s110 respectively acquires the path from the source node to each neighbor node and adds the extended path set.
First, the path P (v)1,v1) Put into binary heap, for source node v1Expanding P (v) outward1,v2) The path is put into a binary heap, the operation number of updating the binary heap is 1, and 1 path is stored in the binary heap.
Then uses the source node v1Path (v) is extended outward1,v5) The number of operations to update the binary heap is 2, and the 2 nd path is stored in the binary heap, and the criticality values of both paths are zero.
S120, according to the sequence from high to low of the weight of the paths in the extended path set, one path is taken out each time and extended according to the breadth of the network topology, and the non-K short paths obtained through extension are added into the extended path set for continuous extension.
Two in binary heapThe criticality values of the paths are all zero, and the taken path may be one of all paths satisfying the same number of constraints, specifically, path P (v) taken from the binary heap1,v2) Paths in binary heap are reduced by 1, and then by v2Store path P (v) as a starting point to expand outward1,v3) Updating the binary heap for 3 times, storing the 2 nd path in the heap, and then using v2Extend the path outward for the starting point (v)2,v6) The number of operations to update the binary heap is 4, and the 3 rd path is stored.
Up to the take-out path P (v)1,v3) The path passes through v1，v2And v3Then with v3Expand outward (v)3,v7) The path is a path in the must-pass resource set, when the path P (v) is1,v7) V passing through1，v2，v3And v7The criticality of this path is 1.
The next time path P (v) with criticality of 1 is taken from the binary heap1,v7) Until it extends to node v10The subsequent path criticality is 2, namely all the specified resources in the necessary resource set I are included, and finally when the path is expanded to the destination node v16Then, a path containing all the specified resources in the necessary resource set I is found and stored in the binary heap as the shortest path set.
S130, judging whether the number K of the paths in the binary heap serving as the shortest path set reaches the specified number K, if so, entering the step S140; if not, the process returns to step S120.
S140, according to the minimum hop count, sorting and outputting the binary heap storing the shortest path set, and ending.
The method for sequencing all paths in the shortest path set comprises the following steps: according to at least one of distance, hop count and delay of the path, or any combination thereof.
The first K paths are the final results, and the path is calculated until the first K short paths are found and then the path is exited. Finally, the shortest paths of 50 pieces meeting the conditions are found, and the method takes 10ms in total. Fig. 4 shows a shortest path that meets the requirements.
In another example, the expand operation on the paths in the expanded path set is repeated until the paths in the expanded path set are all fetched, i.e.:
step S130': and judging whether the extended path set has paths, if so, returning to the step S120, and if not, entering the step S140.
The method gradually expands from the source node to the destination node according to the breadth of the network topology, can ensure that all K short paths meeting the conditions are found, and meanwhile, the convergence speed of path calculation according to the weight of the paths is high, so that the calculation result is obtained quickly.
When the extracted path is expanded, the adjacent node of the tail end node of the extracted path can be expanded each time, an expansion method can be flexibly set according to the actual situation, in addition, the constraint condition can be a necessary node/path, a forbidden node/path and the like, and the requirements of various application scenes are met.
A second embodiment of the present invention provides a method for calculating a K short path, where when an operation on an extended path set reaches an operation upper limit value, the calculation is stopped, and all paths in a shortest path set are sorted and output; the operation on the expanded path set comprises a path taking-out operation, a path adding operation and a path deleting operation.
The K short path calculation method specifically comprises the following steps:
s201 initializes the container U with P (v)s,vs) Is added into a container U, the volume M of the container U cur1, the current number of operations C of the container U cur1, the number of shortest paths K found is 0.
Fetch Path P (v)s,vs) Volume M of the vessel Ucur0, the current number of operations C of the container UcurSequentially adding neighbor paths of the source node into a container U, wherein the size M of the container U is equal to 2 when each neighbor path is insertedcurSelf-increasing 1, CcurSelf-increment by 1. Wherein the neighbor path is a slave source node vsExtend out to source node vsV of a neighbor nodeiThe resulting path P (v)s,vi) Calculating a path P (v)s,vi) The criticality value of the path including L indispensable resources is L, and the path P (v) is divided intos,vi) The principle of inserting a path into a container U to a certain position of the container U is: the paths whose weight is large are arranged in front of the container U, and in the present embodiment, the weight includes criticality.
When the criticality value of the path to be inserted is the same as the maximum criticality value of the paths in the container U, the arrangement order of the paths with the maximum criticality value may be defined according to actual needs, for example, the path to be inserted may be arranged in front of other paths, or in other defining manners.
S202, judging whether elements exist in the container or not, and if not, entering the step S212; if yes, the process proceeds to step S203.
S203 takes out the first element P (v) from the container Us,vi)，CcurSelf-increment by 1.
S204 judges whether or not C is satisfiedcur≥CmaxIf yes, the process goes to step S212, which indicates that the upper limit value of the operation times is reached; otherwise, the process proceeds to step S205.
S205 obtaining from viStarting a link ei＝(vi,vi+1)，vi+1Is v isiOf neighbor nodes, i.e. eiIs P (v)s,vi) The neighbor path of (2).
S206 to prevent looping of the path, judge eiWhether or not it is already included in the path P (v)s,vi) If yes, return to step S205; otherwise, step S207 is executed.
S207 links ei＝(vi,vi+1) Extension to Path P (v)s,vi) In (3), the current path obtained by expansion is P (v)s,vi+1)。
S208 judges whether or not v is satisfiedi+1＝vdAnd P (v)s,vi+1) If the path is a path satisfying the set I, the process proceeds to step S209, and if the path is a path satisfying the set I, the process proceeds to step S210.
S209 calculates path P (v)s,vi+1) And path P (v) is inserted according to the insertion principle described aboves,vi+1) Inserted into the container U, and the process proceeds to step S211.
S210P (v)s,vi+1) Stores it in the output container T and increments the number K of shortest paths that have been found by 1.
S211, judging whether the traversal is finished viIf not, returning to the step S205; if yes, the process returns to step S202.
S212, all paths in the container T are sequenced, the first K paths in the container T are taken out, and the operation is finished.
In this embodiment, the calculation of the paths is completed until the number of operations on the container U reaches a preset upper limit value of the number of operations, and then all the paths in the shortest path set are sorted and output, for example, the upper limit value of the number of operations is 10000 times.
A third embodiment of the present invention provides a method for calculating a K-short path, where on the basis of the second embodiment of the present invention, when the total number of paths in an extended path set reaches a path upper limit value, the calculation is stopped, and all paths in the shortest path set are sorted and output.
Specifically, the method of the second embodiment further counts the total number of paths in the container U during operation until the number of operations on the container U reaches the preset upper limit of the number of operations, or exits when the total number of paths in the container U reaches the preset upper limit of the total number of paths.
When the network size is large, since the path expanding outward layer by layer grows exponentially, the size of the container storing the expanded path and the operation on the container need to be limited. The calculation process is controlled by setting the upper limit value of the operation times or the total number of the paths of the extended path set, and a part of or even all K short paths can be quickly obtained under the condition that the calculation resources (memory) and the calculation time are limited.
A fourth embodiment of the present invention provides a method for calculating a K-short path, which is based on the third embodiment of the present invention and includes, in addition to criticality,the weight of the path also includes the length, cost or delay of the path, using C (e)i) And (4) showing. C (P (v)s,vd))＝∑(vm,vn)∈E)C(vm,vn) Represents the path P (v)s,vd) The weight of (c).
For all paths, determining weights according to the criticality of the paths, wherein the numerical value of the criticality is the number of the constraint conditions met by the paths, and the larger the numerical value of the criticality is, the higher the weight is.
When the key degree values of the multiple paths are the same, the weight of the path further includes at least one of the distance, the hop count and the delay of the path or any combination thereof, and the smaller the distance, the hop count and/or the delay of the path is, the higher the weight is.
A fifth embodiment of the present invention provides a method for calculating a K-short path, where on the basis of any of the above embodiments, all paths in a shortest path set are sorted, and the sorting method includes: according to at least one of distance, hop count and delay of the path, or any combination thereof.
For the network in fig. 1, a sixth embodiment of the present invention provides a method for calculating a K-short path, where the path calculation process is as follows:
the data in the first heap is: 5-2, 5-4, 5-6, 5-8;
the data in the second heap is: 5-4, 5-6, 5-8, 5-2-1, 5-2-3;
the data in the third heap is: 5-4-7, 5-6, 5-8, 5-2-1, 5-2-3, 5-4-1 (when an include node is present, the path including the resource is preferably placed at the head of the heap).
The data in the fourth heap is: 5-4-7-8,5-4-7-4,5-6,5-8,5-2-1,5-2-3,5-4-1.
The subsequent paths will preferably continue to expand along the path containing the mandatory resources until the method is finished. Finally, a group of K short paths containing the necessary resources is calculated.
Since the method of the embodiment of the present invention includes that all the paths of the specified resources of the must-pass resource set I are placed in front of the binary heap, a heap of paths including K must-pass resources is quickly calculated.
The method of the embodiment of the invention has the time complexity of O (C)max logMmax) Spatial complexity of O (M)max). When the network size is small, all the K short paths can be rapidly solved. Compared with the method for assembling the paths obtained by the segmented calculation to obtain the K short paths, the method provided by the embodiment of the invention is simpler and does not need to specify the sequence of the necessary resources.
Compared with the K short path method combined with the shortest path method, the method provided by the embodiment of the invention does not depend on the common shortest path method in network optimization, is a pseudo polynomial time method under the condition of given heap and operation times, and has higher convergence speed under the condition of more sufficient computing resources (memory).
The present invention is not limited to the above-described embodiments, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements are also considered to be within the scope of the present invention. Those not described in detail in this specification are within the skill of the art.
Claims (8)
1. A K short path calculation method is used in the scenes including travel route planning, logistics transportation planning, urban rail transit planning, communication network planning and satellite network data transmission; it is characterized by comprising the following steps:
respectively acquiring paths from a source node to each neighbor node and adding an extended path set;
according to the sequence from high to low of the weight of the paths in the extended path set, taking out one path each time and extending the path to a neighbor node of a tail end node of the taken path according to the width of network topology, adding a non-K short path obtained by extension into the extended path set, continuing to extend until the tail end node of the taken path is a host node, adding the K short path obtained by extension into the shortest path set, and outputting the shortest path set in sequence;
the weight of the path comprises criticality, and the numerical value of the criticality is the number of the constraint conditions met by the path;
the non-K short path is a path of which the extended path does not meet all constraint conditions when the extension is performed from the source node to the sink node in a grading manner; or a path that satisfies all constraints but has not yet reached the sink node;
the path taken out each time is one path which meets the most constraint conditions or one of all paths which meet the same number of constraint conditions;
the constraints include must-pass nodes, must-pass links, forbidden nodes, and forbidden paths.
2. The method of calculating a K-short path as claimed in claim 1, wherein: when the criticality values of the plurality of paths are the same, the weight of the path further includes at least one of a distance, a hop count, and a delay of the path, or any combination thereof.
3. The method of calculating a K-short path as claimed in claim 1, wherein: the extended path set is a binary heap, and paths with high weights are stored at the head of the binary heap.
4. The method of calculating a K-short path as claimed in claim 1, wherein: each time a path is taken, if the path is looped, it is discarded.
5. The method of computing a K-short path as recited in claim 1, the method further comprising: repeating the expanding operation of the paths in the expanded path set until the total number of the paths in the shortest path set is K, or all the paths in the expanded path set are taken out.
6. The method of computing a K-short path as recited in claim 1, the method further comprising: when the operation on the extended path set reaches an operation upper limit value, stopping calculation, and sequencing and outputting all paths in the shortest path set;
the operation on the expansion path set comprises a taking path, a joining path and a deleting path.
7. The method of computing a K-short path as recited in claim 1, the method further comprising: and when the total number of the paths in the extended path set reaches the path upper limit value, stopping calculation, and sequencing all the paths in the shortest path set and outputting the sequenced paths.
8. The method of computing K-short paths of claim 1, wherein the method of ordering all paths in the shortest path set is: according to at least one of distance, hop count and delay of the path, or any combination thereof.
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