CN103150219B - Heterogeneous resource system is avoided the fast worktodo distribution method of deadlock - Google Patents

Abstract

The present invention relates to a kind of fast worktodo distribution method avoiding deadlock in heterogeneous resource system.Comprising the following steps, 1, concrete application uses the expression of task data flow graph, utilize the adjacency matrix geometric operation of task data flow graph to obtain new matrix, this new matrix is for representing that whether the length of internodal longest path is more than or equal to 2；2, select between node, according to new matrix, the node pair that longest path length is less than 2, amount of communication data is maximum, node is combined into node cluster；Update this new matrix, repeat the process that above-mentioned node merges, reduce the scale of task data flow graph to specifying target；3, utilize integral linear programming equation collection, distribute this task data flow graph and close to heterogeneous resource collection.Present invention have the advantage that: there is the communication dependence between the dependence of tasks carrying priority, task and avoid the feature of deadlock, it is achieved that the overhead of heterogeneous resource system minimizes.

Description

Heterogeneous resource system is avoided the fast worktodo distribution method of deadlock

Technical field

The present invention relates to extensive task distribution on a kind of heterogeneous cluster, be specifically related to a kind of in heterogeneous resource system Avoid the fast worktodo distribution method of deadlock.

Background technology

The scientific computer system of modern high performance and universal BCS are nearly all based on heterogeneous cluster Computer Systems Organization.In heterogeneous computer system, same type of processor is interconnected and form a group of planes, different group of planes Between be connected by the communication link of isomery.Heterogeneous cluster is provided that the highest computational efficiency, and using huge expense as generation Valency.

In heterogeneous resource system, extensive task completes on various types of other heterogeneous resource, work in coordination with a large amount of Different classes of heterogeneous resource completes an extensive task jointly.Fig. 1 show heterogeneous resource system model schematic diagram, rectangle Representing heterogeneous resource kind, circle represents heterogeneous resource, and the passage between rectangle represents communication link.Variety classes heterogeneous resource cl₁、cl₂、cl₃In heterogeneous resource have different performances and energy consumption, heterogeneous resource kind cl₁、cl₂、cl₃Between on communication link The call duration time of transmission data is the most variant with energy consumption.Therefore, extensive task is effectively allocated on various heterogeneous resource, Make on the premise of meeting time-constrain, reduce the significant challenge that system overhead is heterogeneous resource research field.And at isomery In resource system, extensive task was distributed in addition to the execution time needing consideration task and expense, it is also desirable to consider transmission Time and expense.

In heterogeneous resource system, the distribution of large-scale task is np hard problem, and the search volume of solution is huge, anxious Need to study and find optimum or the efficient solutions of approximate optimal solution in the short time.More existing technology are used for solving task expense Minimization problem, but they do not account for the communication dependence between task dependence successively, task, and local adjust Degree avoids the safety of deadlock.

Summary of the invention

The technical problem to be solved is just to provide a kind of avoid deadlock in heterogeneous resource system quick Business distribution method, it has the communication dependence between the dependence of task priority, task and avoids deadlock, and can realize different The overhead of structure resource system minimizes.

The technical problem to be solved is realized by such technical scheme, and it comprises the following steps:

Step 1, concrete application is used the expression of task data flow graph, utilize the adjacency matrix of task data flow graph The new matrix of geometric operation, this new matrix is for representing that whether the length of internodal longest path is more than or equal to 2；

Step 2, select between node, according to new matrix, the node pair that longest path length is less than 2, amount of communication data is maximum, Node is combined into node cluster；Update this new matrix, repeat the process that above-mentioned node merges, reduce the scale of task data flow graph To specifying target；

Step 3, utilize integral linear programming equation collection, distribute this task data flow graph and close to heterogeneous resource collection.

Owing to the present invention implements task distribution according to task data flow graph, possesses the dependence that task successively performs completely Communication dependence between relation, task；Owing to the present invention reduces the scale of task data flow graph, task distribution can be effectively improved Efficiency；During the scale reducing task data flow graph, longest path length between node is selected to be less than the node of 2 to entering Row merges, it is to avoid loop generation, it is ensured that deadlock will not occur during local scheduling；The present invention utilizes integral linear programming Equation collection, can find task node to be assigned to the optimal solution of heterogeneous resource.So present invention have the advantage that: have and appoint Business performs the communication dependence between dependence successively, task and avoids the feature of deadlock, it is achieved that heterogeneous resource system Overhead minimize.

Accompanying drawing explanation

The accompanying drawing of the present invention is described as follows:

Fig. 1 is heterogeneous resource system model schematic diagram；

Fig. 2 is the task data flow graph of a large-scale application；

Fig. 3 is the flow chart of the reduction task data flow graph scale of the present invention；

Fig. 4 is the process example figure of the reduction task data flow graph scale of the present invention.

Detailed description of the invention

The conception of the present invention is: the node of task data flow graph is merged into node cluster.If but be made up of node cluster New task data flow graph have loop, then may produce deadlock in task scheduling process.Number of tasks at directed acyclic According in flow graph, the essential condition producing loop after two nodes are merged into a node cluster is to deposit between above-mentioned two node In the path more than or equal to 2.And an available new matrix after adjacency matrix is carried out geometric operation, by this new matrix Matrix element may determine that the path that whether there is certain length between node.To this, we illustrate a series of definition, reason Opinion, and carried out mathematical proof.

Using task data flow graph representation to be existing technological means one application task, list of references has: Shao Efficiently distribution in ZL, Zhuge QF, Xue C, Sha HM. isomery dsp system is parallel with scheduling research [J] .IEEE with distribution Formula system transactions, the 16th phase, volume 6, page 516 to 525 (Shao ZL, Zhuge QF, Xue C, Sha HM, Efficient assignment and scheduling for heterogeneous dsp systems[J].IEEE Transactions On Parallel and Distributed Systems, 2005,16 (6): 516 525.).

The invention will be further described below in conjunction with the accompanying drawings:

The fast worktodo distribution method avoiding deadlock in heterogeneous resource system of the present invention, comprises the following steps:

Step 1, concrete application being used task data flow graph representation, the adjacency matrix utilizing task data flow graph is several What computing obtains new matrix, and this new matrix is for representing that whether the length of internodal longest path is more than or equal to 2；

Step 2, select between node, according to new matrix, the node pair that longest path length is less than 2, amount of communication data is maximum, Node is combined into node cluster；Update this new matrix, repeat the process that above-mentioned node merges, reduce the scale of task data flow graph To specifying target；

Step 3, utilize integral linear programming equation collection, distribute this task data flow graph and close to heterogeneous resource collection.

Mathematical definition heterogeneous resource system is Clus=<CL, CT, CC>, wherein the species number of heterogeneous resource is | CL |, always The mathematical definition of heterogeneous resource set be CL={cl₁,cl₂,…,cl_|CL|, unit call duration time between heterogeneous resource set Collection is combined into

$CT=\{{\mathrm{ct}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_1},{\mathrm{ct}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_2},...,{\mathrm{ct}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|-1}},{\mathrm{ct}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|}}\},$

The collection of unit communication energy consumption is combined into

$CC=\{{\mathrm{CC}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_1},{\mathrm{CC}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_2},...,{\mathrm{CC}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|-1}},{\mathrm{CC}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|}}\}$

Fig. 2 is the task data flow graph of an extensive task, and circle represents task, and directed edge represents dependence between task And have data communication.

Mathematical definition has the task data flow graph of weight to be G=<V, E, D>it is a directed acyclic graph, by the individual node of | V | Form with | E | bar directed edge；V={v₁,v₂,…,v_|V|Representing node set, each node represents a task；It is the set on limit, represents the dependence of set V interior joint, $D=\{d_{v_1,v_1},d_{v_1,v_2},...,d_{v_{\left|V\right|},v_{\left|V\right|-1}},d_{v_{\left|V\right|},v_{\left|V\right|}}\}$ Represent the set of inter-node communication data volume.

Boolean's adjacency matrix of mathematical definition task data flow graph G is A, for matrix A, element a_i,j=1 represents in data Flow graph G exists from node i to j directed edge；Mathematical definition Boolean matrix set { A²、A³…A^|V|-1, for one of them square Battle array A^p, elementRepresenting the path that there is a length of p bar limit from node i to j, wherein, p is greater than equal to 2 and is less than Integer in | V |-1；The new matrix A of mathematical definition boolean^≥2, new matrix elementRepresent and arrive at task data flow diagram G interior joint i Whether the longest path of node j is more than or equal to 2.WhenTime represent node i arrive the length of node j longest path more than or Equal to 2, whenTime represent that node i arrives the length of node j longest path less than 2.

Fig. 3 is the flow chart of the reduction task data flow graph scale of the present invention, and this flow process starts from step 301, then:

In step 302, incoming task data flow diagram G=<V, E, D>, the adjacency matrix A of G, and the node number of clusters of target Amount obj；

In step 303, Initialize installation, all nodes in figure G as the node cluster being made up of individual node；

In step 304, initially set the numerical value p of enumerator P as 2；

In step 305, it is judged that whether p reaches boundary value | V |-1, and wherein, | V | represents the number of nodes of figure G, if p is not Reach | V |-1, then perform step 306, if p reaches | V |-1, then perform step 308；

In step 306, utilize A^p-1It is multiplied with A and obtains A^p, specifically, A^pIn matrix, the calculating formula of element is $a_{i,j}^p=(a_{i,1}^{p-1}\&times;a_{1,j})+...+(a_{i,\left|V\right|-1}^{p-1}\&times;a_{\left|V\right|-1,j})+(a_{i,\left|V\right|}^{p-1}\&times;a_{\left|V\right|,j}),$ Wherein,A is respectively matrix A^p、A^p-1, the matrix element of A, i with j represents more than or equal to 1 and is less than or equal to the integer of | V |；

In step 307, enumerator P adds up 1, returns step 305；

In step 308, it is calculated matrix A^|V-1|；

In step 309, it is calculated matrix A^≥2, specifically, A^≥2The calculating formula of the element in matrix isWherein,It is respectively matrix A^≥2、A²、A³、A^|V|-1's Matrix element, i with j represents more than or equal to 1 and is less than or equal to the integer of | V |；

In step 310, arrange and deposit variable G ', A ', A '^≥2, respectively task data flow graph G, the adjacency matrix A of input And calculated A^≥2It is stored in；

In step 311, it is judged that whether figure G ' exists limit, if not existing, then perform step 312；If existing, then perform step 313；

In step 312, arbitrarily choose 2 node clusters i, j at figure G ', then perform step 315；

In step 313, figure G ' finds node cluster to i, j；

In step 314, it may be judged whether meet conditionAnd meeting all node cluster centerings of this condition, i, j Between data traffic maximum；If the node cluster being currently found is to meeting above-mentioned condition, then perform step 315；If currently looking for To node cluster to being unsatisfactory for above-mentioned condition, then return step 313；

In step 315, merging node cluster, to i, j, obtains node cluster i'；

In step 316, according to combination situation, update figure G ', update adjacency matrix A ', update matrix A '^≥2；Figure G ' is more Newly, the most in the drawings must merge node cluster i, j with ring to together；

Matrix A ' renewal specifically, new A ' matrix is by obtaining from old A ' matrix calculus, specifically, the of new A ' matrix I row matrix element can pass through calculating formula a '_i,k=a '_i,k∨a’_j,kObtaining, the matrix element of jth row can pass through calculating formula a’_k,j=a '_k,i∨a’_k,jObtain, wherein k ∈ [1, | V |] and supposition i < j.Remaining matrix element is copied afterwards from old A ' matrix On the correspondence position of new A ' matrix, the jth row finally deleted on new A ' matrix arranges with jth.

Matrix A '^≥2Renewal as the renewal process of A ', but, each node cluster merges may increase length Path more than or equal to 2, it is also possible to the extra minimizing length path more than or equal to 2.Only by merging old A '^≥2Unit in matrix Element is calculated new A '^≥2, it has been ignored as this point above-mentioned.Therefore, by old A '^≥2It is new that matrix obtains after merging matrix element A’^≥2In, need to reset some elements, i.e. perform step 317；

In step 317, meet for all,And the longest path from i' to x is less than the feelings of 2 the two conditions Condition, givesCompose 0 value, wherein, x ∈ V',Meet for all,And the longest path from y to i' Less than the situation of 2 the two conditions, giveCompose 0 value, wherein, y ∈ V',Meet for all, And the longest path from x to y is more than or equal to the situation of 2 the two conditions, givesCompose 1 value, wherein, x, y ∈ V', ${a^{\&prime;}}_{x,y}^{\&GreaterEqual;2}\&Element;A^{\&prime;\&GreaterEqual;2};$

In step 318, it is judged that whether current node cluster quantity reaches desired value obj, if being not reaching to, then return step 311；If reaching, then perform step 319；

In step 319, utilize integral linear programming equation to integrate and be quickly found out the distribution of efficient task as task data flow graph G ' Scheme, concrete equation collection given below:

Constraint 1: each task node can only be mapped to a kind of heterogeneous resource set

$\begin{array}{cc}\underset{i\&Element;CL}{\&Sigma;}Map(v,i)=1& \&ForAll;v\&Element;V\end{array}---\left(1\right)$

Constraint 2: transmit the kind of selected heterogeneous resource set for the data between task node

$\begin{array}{c}2BMap(u,v,i,j)-1\&le;Map(v,i)+Map(v,j)-1\\ \begin{array}{cc}\&le;BMap(u,v,i,j)& \&ForAll;(u,v)\&Element;E,i\&Element;CL,j\&Element;CL\end{array}\end{array}---\left(2\right)$

Constraint 3: each task node must wait its predecessor task node to complete could start to perform

$\begin{array}{c}F\left(u\right)+\underset{i\&Element;CL}{\&Sigma;}\underset{j\&Element;CL}{\&Sigma;}\&lsqb;BMap(u,v,i,j)\&times;d_{u,v}\&times;{\mathrm{ct}}_{i,j}\&rsqb;+\\ \begin{array}{cc}\underset{i\&Element;CL}{\&Sigma;}\&lsqb;Map(v,i)\&times;t_{v,i}\&rsqb;\&le;F\left(v\right)& \&ForAll;(u,v)\&Element;E\end{array}\end{array}---\left(3\right)$

The execution time of 4: one task node early starts of constraint is in the moment 0, and this condition is only for not entering limit Task node be necessary

$\begin{array}{cc}\underset{i\&Element;CL}{\&Sigma;}\&lsqb;Map(v,i)\&times;t_{v,i}\&rsqb;\&le;F\left(v\right)& \&ForAll;v\&Element;V\end{array}---\left(4\right)$

Constraint 5: all task nodes must complete before maximum execution time L

$\begin{array}{cc}F\left(v\right)\&le;L& \&ForAll;v\&Element;V\end{array}---\left(5\right)$

Constraint 6: the node in same node cluster must be assigned in same type heterogeneous resource set；

Object function: overhead minimizes.

For given task data flow graph, overhead is equal between executive overhead and the task node of all task nodes The superposition of communication overhead；Total execution time of this Flow chart task is that root node starts to go to last task node and completes to hold The time of row spends:

$\begin{array}{c}\min \underset{(u,v)\&Element;E}{\&Sigma;}\underset{i\&Element;CL}{\&Sigma;}\underset{j\&Element;CL}{\&Sigma;}\&lsqb;BMap(u,v,i,j)\&times;d_{u,v}\&times;{\mathrm{cc}}_{i,j}\&rsqb;\\ +\underset{v\&Element;V}{\&Sigma;}\underset{i\&Element;CL}{\&Sigma;}\&lsqb;Map(v,i)\&times;c_{v,i}\&rsqb;\end{array}---\left(6\right)$

In formula, d_u,vRepresent the amount of communication data of node u to node v, cc_i,jRepresent resource collection i to resource collection j transmission The communication overhead of unit data, ct_i,jRepresent the call duration time of resource collection i to resource collection j unit of transfer data.

The deadline of function F (v) record node v,Codomain is arithmetic number, and definition territory is set V.

Function Map (v, i), whether definition node v is mapped to resource collection i,i∈CL.Definition territory is set V And the combination of set CL, the size in definition territory is | V | × | CL |, and codomain is 0 and 1；(v, the necessary and sufficient condition of i)=1 is joint to Map Point v is mapped to resource collection i.

Function BMap (u, v, i, j), codomain is made up of 0 and 1,BMap(u,v,i,j) =1 necessary and sufficient condition set up is that node u is mapped to resource collection i and node v is mapped to resource collection j.

SetIt it is execution time of closing at different resource collection of each node Set, t_vi,cljRepresent node v_iIf being mapped to cl_jOn the execution time.

SetIt is that the execution that each node closes at different resource collection is opened Pin set,Represent node v_iIf being mapped to cl_jOn executive overhead.

After completing step 319, then perform step 320 and terminate.

One access request, after starting flow process shown in Fig. 3 and completing, is achieved that and avoids deadlock on heterogeneous resource Fast worktodo distribution.

Reduce the correctness of the step of task data flow graph scale, illustrate with 2 inferences by providing 3 theorems:

Theorem 1: the task data flow graph G=<V, E, D of given directed acyclic>, assemble any two node i, j (i, j ∈ V) becoming 1 node cluster, the necessary and sufficient condition newly scheming to exist in G ' loop of generation is to have at least one between figure G interior joint i and j The bar length path more than 1, i.e. this path, at least through 1 node x ∈ V, meets x ≠ i, x ≠ j.

Prove: if node is merged into a node cluster to i Yu j, if there is a paths between i and j through at least One node x, wherein x ≠ i, x ≠ j, then the figure G ' obtained after merging node necessarily has ring.If it addition, between i and j Path the most by other nodes, then the figure G ' obtained after merging node does not the most have ring.Therefore, if obtained after He Binging To G ' have ring, then at least there is a paths between i and j through node x, wherein x ≠ i, x ≠ j.

Inference 1: a given task data flow graph G=<V, E, D>, and adjacency matrix A, for any one group node u, V ∈ V, ifWithBe all 0, then the G ' that newly schemes that node u Yu v obtains after assembling does not has a loop, wherein,WithAll It is A^≥2Matrix element.

Theorem 2: be not the task data flow graph G=<V, E, D of the directed acyclic of 0 for the quantity on limit>and the adjacent square of G Battle array is A, at least there is a pair node u, v ∈ V, meets a_u,v=0, wherein, a_u,v∈A^≥2。

Prove: we will prove by inductive method.

It is initial: if the task data flow graph of a directed acyclic is made up of 2 nodes and the quantity on limit is not 0, then this figure Middle necessarily only exist a paths and a length of 1.Now theorem 2 is set up.

Recursion step: assume that, when the nodes of task data flow graph is k, this theorem is set up, i.e. the most at least have one To node i, j, meet a_i,j ^≥2=0, wherein k >=2, a_i,j ^≥2∈A^≥2And 1≤i, j≤| V |.Then when this figure increases by 1 node Time, it will there are two kinds of situations.

In the first situation, there is, between+1 node of kth with k node before, the limit being connected, i.e. in kth+1 Path is there is between individual node and node before.Assume that the length in these paths is both greater than 1, and assume node i (i ∈ V and 1≤i ≤ k) to the path of node k+1 more than 1, therefore must be through a node j (1≤j≤k) on the path of i to k+1；And by Be both greater than 1 in the length setting these paths, then another node m (1≤m≤k) must be passed through in the path of node j to k+1.According to this Sample repeats down, owing to also having k-1 node in figure in addition to node i with node k+1, therefore in-1 node x of kth (x ∈ V and 1 ≤ x≤k) be utilized after, it is impossible to find a node to make the path of x to k+1 more than 1 and not produce loop again.Therefore, Node k+1 and before k node between at least there is the path of a length of 1, i.e. at least there is a pair node and meet(or), wherein, (x ∈ V and 1≤x≤k).Therefore in the first situation, this theorem is set up.

In second case, there is not, between node k+1 with k node before, the limit being connected.So, at least exist A pair node meetsCondition because k node before has met this condition the most, wherein,And i ≠ j.Therefore in second case, this theorem is set up.

Inference 2: for the task data flow graph of any directed acyclic, can merge at least one pair of node, obtains one newly The task data flow graph of directed acyclic.

Theorem 3: for the task data flow graph G=<V, E, D of given directed acyclic>, G can be compressed into arbitrary node The new directed acyclic graph of number of clusters amount.

Prove: according to inference 2, the scale of any given directed acyclic graph G can reduce 1 and obtain a new directed acyclic Figure.We can repeat above-mentioned action until being reduced to the scale of target.

Conclusions has been summed up following 4 points:

1) if 1 couple of node cluster i, j meetIt is the condition of 0, then merges i, j to one node cluster and will not produce loop, Wherein(theorem 1 and inference 1)

2) for any given task data flow graph, we can find 1 pair of node cluster to meet merging condition.(theorem 2)

3) according to above-mentioned condition merge 1 to node cluster after, the quantity of node cluster will subtract 1, as inference 2 is sayed, can obtain one Individual new task data flow graph.

4) any one task data flow graph total energy reduces scale to desired value.(theorem 3)

Fig. 4 is the process example figure of the reduction task data flow graph of the present invention, and in figure, (a) is given task data flow Figure, (e) is the A of task data flow graph in corresponding (a)^≥2Matrix；B (), (c), (d) are to subtract small-scale number of tasks step by step According to flow graph, the A of task data flow graph in (f), (g), (h) the most corresponding (b), (c), (d)^≥2Matrix.

Target is that the figure in Fig. 4 (a) is merged into the figure being made up of 3 node clusters.Before the combining, A^≥2Such as Fig. 4 (e) Shown in, every pair of connected node can merge, and node is to there being the amount of communication data of maximum between E, F, and therefore the 1st time E, F Merge E ' in groups.Shown in amalgamation result such as Fig. 4 (b).Merge node C and node group E 2nd time ' obtain node group C ', such as Fig. 4 (c) Shown in.According to Fig. 4 (g), the 3rd time merge select node to A, B because A, B meetCondition and between logical Letter data amount is maximum of which.Therefore, shown in final task data flow graph such as Fig. 4 (d).

Claims (2)

1. in heterogeneous resource system, avoid the fast worktodo distribution method of deadlock, it is characterized in that, comprise the following steps:

Step 1, concrete application is used the expression of task data flow graph, utilize the adjacency matrix geometry of task data flow graph Computing obtains new matrix, and this new matrix is for representing that whether the length of internodal longest path is more than or equal to 2；

Step 2, select between node, according to new matrix, the node pair that longest path length is less than 2, amount of communication data is maximum, node It is combined into node cluster；Update this new matrix, repeat the process that above-mentioned node merges, reduce the scale of task data flow graph to referring to Set the goal；

The mathematical definition of heterogeneous resource system is Clus=<CL, CT, CC>, wherein the species number of heterogeneous resource is | CL |, total The mathematical definition of heterogeneous resource set is CL={cl₁,cl₂,…,cl_|CL|, between heterogeneous resource, the collection of unit call duration time is combined into

$CT=\{{\mathrm{ct}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_1},{\mathrm{ct}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_2},...,{\mathrm{ct}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|-1}},{\mathrm{ct}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|}}\},$

The collection of unit communication energy consumption is combined into

$CC=\{{\mathrm{cc}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_1},{\mathrm{cc}}_{{\mathrm{cl}}_1,{\mathrm{cl}}_2},...,{\mathrm{cc}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|-1}},{\mathrm{cc}}_{{\mathrm{cl}}_{\left|CL\right|},{\mathrm{cl}}_{\left|CL\right|}}\};$

The mathematical definition of task data flow graph is a directed acyclic graph G=<V, E, D>, by the individual node of | V | and | E | bar directed edge Composition；V={v₁,v₂,…,v_|V|Representing node set, each node represents a task； It is the set on limit, represents the dependence of set V interior joint,Represent between node The set of amount of communication data；

Boolean's adjacency matrix of mathematical definition task data flow graph G is A；Mathematical definition Boolean matrix set { A²、A³…A^|V|-1, For one of them matrix A^p, elementRepresenting the path that there is a length of p bar limit from node i to j, wherein, p is greater than Equal to 2 and be less than or equal to the integer of | V |-1；The new matrix A of mathematical definition boolean^≥2, new matrix elementRepresent in task data Whether the longest path of flow graph G interior joint i to node j is more than or equal to 2；

It is calculated set of matrices A^p, utilize A^p-1It is multiplied with A and obtains A^p, specifically, A^pIn matrix, the calculating formula of element isWherein,A is respectively matrix A^p、A^p-1, the matrix element of A, i with j represents more than or equal to 1 and is less than or equal to the integer of | V |；

It is calculated new matrix A^≥2, A^≥2In element calculating formula beWherein,It is respectively matrix A^≥2、A²、A³、A^|V|-1Matrix element, i Yu j all represent more than or equal to 1 and It is less than or equal to the integer of | V |；

All nodes in task data flow graph G as the node cluster being made up of individual node, arrange and deposit variable G ', A ', A ’^≥2, respectively task data flow graph G, adjacency matrix A and the calculated new matrix A of input^≥2It is stored in；

Deposit at figure and variable G ' finds node cluster to i, j, deposit variables A according to new matrix '^≥2Judge to meet conditionAnd meeting all node cluster centerings of this condition, data traffic between i, j is maximum, merge node cluster to i, J, obtains node cluster i'；

Step 3, utilize integral linear programming equation collection, distribute this task data flow graph and close to heterogeneous resource collection；

For given task data flow graph, overhead communicates equal between the executive overhead of all task nodes and task node The superposition of expense；Total execution time of this Flow chart task is that root node starts to go to last task node and completes to perform Time spends, and overhead is minimum:

$\begin{array}{c}min\underset{\left(u,v\right)\&Element;E}{\mathrm{\&Sigma;}}\underset{i\&Element;CL}{\mathrm{\&Sigma;}}\underset{j\&Element;CL}{\mathrm{\&Sigma;}}\&lsqb;BMap\left(u,v,i,j\right)\&times;d_{u,v}\&times;{\mathrm{cc}}_{i,j}\&rsqb;\\ +\underset{v\&Element;V}{\mathrm{\&Sigma;}}\underset{i\&Element;CL}{\mathrm{\&Sigma;}}\&lsqb;Map\left(v,i\right)\&times;c_{v,i}\&rsqb;\end{array}$

In formula, d_u,vRepresent the amount of communication data of node u to node v；

cc_i,jRepresent the communication overhead of resource collection i to resource collection j unit of transfer data；

Function BMap (u, v, i, j), codomain is made up of 0 and 1,BMap (u, v, i, j)=1 one-tenth Vertical necessary and sufficient condition is that node u is mapped to resource collection i and node v is mapped to resource collection j；

Function Map (v, i), whether definition node v is mapped to resource collection i,i∈CL；Definition territory be set V and The combination of set CL, the size in definition territory is | V | × | CL |, and codomain is 0 and 1；(v, the necessary and sufficient condition of i)=1 is node v to Map It is mapped to resource collection i.

Method the most according to claim 1, is characterized in that: after merging node cluster is to i, j, updates figure G ', its adjacent square Battle array A ' and matrix A '^≥2；

It is that node cluster i, j ring in the drawings palpus merged is to together that figure deposits the renewal of variable G '；

Matrix A ' be updated to, the i-th row matrix element of new A ' matrix pass through calculating formula a '_i,k=a '_i,k∨a’_j,kObtain, jth The matrix element of row is by calculating formula a '_k,j=a '_k,i∨a’_k,jObtain, wherein k ∈ [1, | V |] and supposition i < j；Afterwards from old A ' Matrix copies remaining matrix element on the correspondence position of new A ' matrix, finally deletes the jth row on new A ' matrix and jth Row；

Matrix A '^≥2Be updated to, new A '^≥2I-th row matrix element of matrix passes through calculating formula Obtaining, the matrix element of jth row is by calculating formula a '^≥2 _k,j=a '^≥2 _k,i∨a’^≥2 _k,jObtain, wherein k ∈ [1, | V |] and supposition i <j；Afterwards from old A '^≥2Matrix copies remaining matrix element to new A '^≥2On the correspondence position of matrix, finally delete new A '^≥2Square Jth row in battle array arranges with jth；

At more newly obtained new A '^≥2In matrix, reset part matrix element, meet for allAnd from i' to x Long path, less than the situation of 2 the two conditions, is givenCompose 0 value, wherein, x ∈ V',Meet for allAnd the longest path from y to i' is less than the situation of 2 the two conditions, givesCompose 0 value, wherein, y ∈ V',Meet for allAnd the longest path from x to y is more than or equal to the situation of 2 the two conditions, givesCompose 1 value, wherein, x, y ∈ V',