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An Associative Program for the MST Problem using ClearSpeed

An Associative Program for the MST Problem using ClearSpeed. Hassan AL- Maksousy halmakso@kent.edu. a. 2. 8. 7. b. c. 4. 3. 9. 6. e. d. 3. f. Graph used for Data Structure. Figure 6 in [Potter, Baker, et. al.]. current_best$. candidate$. node$. parent$. mask$. PEs. d$.

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An Associative Program for the MST Problem using ClearSpeed

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  1. An Associative Program for the MST Problem using ClearSpeed Hassan AL-Maksousy halmakso@kent.edu

  2. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  3. current_best$ candidate$ node$ parent$ mask$ PEs d$ c$ e$ b$ f$ a$ a ∞ 2 8 ∞ ∞ ∞ b 2 ∞ 7 4 3 ∞ c 8 7 ∞ ∞ 6 9 IS d ∞ 4 ∞ ∞ 3 ∞ a e ∞ 3 6 3 ∞ ∞ root next- node f ∞ ∞ 9 ∞ ∞ ∞ Data Structure for MST Algorithm

  4. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  5. current_best$ candidate$ node$ parent$ mask$ PEs d$ c$ e$ b$ f$ a$ no a ∞ 2 8 ∞ ∞ ∞ b 2 ∞ 7 4 3 ∞ yes a 2 c 8 7 ∞ ∞ 6 9 yes a 8 IS d ∞ 4 ∞ ∞ 3 ∞ wait a e ∞ 3 6 3 ∞ ∞ wait root next- node b f ∞ ∞ 9 ∞ ∞ ∞ wait Data Structure for MST Algorithm

  6. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  7. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  8. current_best$ candidate$ node$ parent$ mask$ PEs d$ c$ e$ b$ f$ a$ no a ∞ 2 8 ∞ ∞ ∞ b 2 ∞ 7 4 3 ∞ no a 2 c 8 7 ∞ ∞ 6 9 yes b 7 IS d ∞ 4 ∞ ∞ 3 ∞ yes b 4 a e ∞ 3 6 3 ∞ ∞ yes b 3 root next- node e f ∞ ∞ 9 ∞ ∞ ∞ wait Data Structure for MST Algorithm

  9. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  10. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  11. current_best$ candidate$ node$ parent$ mask$ PEs d$ c$ e$ b$ f$ a$ no a ∞ 2 8 ∞ ∞ ∞ b 2 ∞ 7 4 3 ∞ no a 2 c 8 7 ∞ ∞ 6 9 yes e 6 IS d ∞ 4 ∞ ∞ 3 ∞ yes e 3 a e ∞ 3 6 3 ∞ ∞ no b 3 root next- node d f ∞ ∞ 9 ∞ ∞ ∞ wait Data Structure for MST Algorithm

  12. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  13. current_best$ candidate$ node$ parent$ mask$ PEs d$ c$ e$ b$ f$ a$ no a ∞ 2 8 ∞ ∞ ∞ b 2 ∞ 7 4 3 ∞ no a 2 c 8 7 ∞ ∞ 6 9 yes e 6 IS d ∞ 4 ∞ ∞ 3 ∞ no e 3 a e ∞ 3 6 3 ∞ ∞ no b 3 root next- node c f ∞ ∞ 9 ∞ ∞ ∞ wait Data Structure for MST Algorithm

  14. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  15. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  16. current_best$ candidate$ node$ parent$ mask$ PEs d$ c$ e$ b$ f$ a$ no a ∞ 2 8 ∞ ∞ ∞ b 2 ∞ 7 4 3 ∞ no a 2 c 8 7 ∞ ∞ 6 9 no e 6 IS d ∞ 4 ∞ ∞ 3 ∞ no e 3 a e ∞ 3 6 3 ∞ ∞ no b 3 root next- node f f ∞ ∞ 9 ∞ ∞ ∞ yes Data Structure for MST Algorithm c 9

  17. a 2 8 7 b c 4 3 9 6 e d 3 f Graph used for Data Structure Figure 6 in [Potter, Baker, et. al.]

  18. Short Version of Algorithm: ASC-MST-PRIM(root) • Initialize candidates to “waiting” • If there are any finite values in root’s field, • set candidate$ to “yes” • set parent$ to root • set current_best$ to the values in root’s field • set root’s candidate field to “no” • Loop while some candidate$ contain “yes” • for them • restrict mask$ to mindex(current_best$) • set next_node to a node identified in the preceding step • set its candidate to “no” • if the value in their next_node’s field are less than current_best$, then • set current_best$ to value in next_node’s field • set parent$ to next_node • if candidate$ is “waiting” and the value in its next_node’s field is finite • set candidate$ to “yes” • set parent$ to next_node • set current_best to the values in next_node’s field

  19. Algorithm: ASC-MST-PRIM • Initially assign any node to root. • All processors set • candidate$ to “wait” • current-best$ to  • the candidate fieldfor the root node to “no” • All processors whose distance d from their node to root node is finite do • Set their candidate$ field to “yes • Set their parent$ field to root. • Set current_best$ = d.

  20. Algorithm: ASC-MST-PRIM (cont. 2/3) • While the candidate field of some processor is “yes”, • Restrict the active processors to those whose candidate field is “yes” and (for these processors) do • Compute the minimum value x of current_best$. • Restrict the active processors to those with current_best$ = x and do • pick an active processor, say node y. • Set the candidate$ value of node y to “no” • Set the scalar variable next-node to y.

  21. Algorithm: ASC-MST-PRIM (cont. 3/3) • If the value zin the next_node column of a processor is less than its current_best$ value, then • Set current_best$ to z. • Set parent$ to next_node • For all processors, if candidate$ is “waiting” and the distance of its node from next_node y is finite, then • Set candidate$ to “yes” • Set current_best$ to the distance of its node from y. • Set parent$ to y

  22. MST in Cn By Hassan AL-Maksousy • //All active processor set current_best to infinit • (*node).current_best = 32; • for(i=0;i<6;i++) • { • (*node).nodeArray[i]=32; • } • if (get_penum() == 0) • { • (*node).nodeId = 'a'; • (*node).nodeArray[1] = 2; • (*node).nodeArray[2] = 8; • } • if (get_penum() == 1) • { • (*node).nodeId = 'b'; • (*node).nodeArray[0] = 2; • (*node).nodeArray[2] = 7; • (*node).nodeArray[3] = 4; • (*node).nodeArray[4] = 3; • } • if (get_penum() == 2) • { • (*node).nodeId = 'c'; • //---------------------------------------------------------- • // mst.cn • // by Hassan AL-Maksousy • // 2012-02-02 • //---------------------------------------------------------- • #include <lib_ext.h> • #include <stdiop.h> • #include "asc.h" • struct nodes • { • char nodeId; • char candidate; • int nodeArray[6]; • int current_best; • int parent; • }; • //---------------------------------------------------------- • void initialize(poly struct nodes* node) • { • poly int i; • //Initialize candidates to 'waiting' • (*node).candidate = 'w'; • (*node).parent = -1;

  23. MST in Cn By Hassan AL-Maksousy • //---------------------------------------------------------- • void showNodes(poly struct nodes node) • { • poly char letter[7]={' ','a','b','c','d','e','f'}; • //Print nodeID, candidate, parent, and current best //distance. • printfp("Node %c: Candidate %c, Parent: %c, Current Best: %d\n" • , node.nodeId • , node.candidate • , letter[node.parent+1] • , ((node.current_best < 32) ? node.current_best : 0) • ); • printf("\n"); • } //End of showNodes(poly struct nodes) • //---------------------------------------------------------- • int main() • { • poly int mask = 0; • //Initially assign any node to root. • poly int root = 0; // we choose the root here // a • poly int minimum = 0; • (*node).nodeArray[0] = 8; • (*node).nodeArray[1] = 7; • (*node).nodeArray[4] = 6; • (*node).nodeArray[5] = 9; • } • if (get_penum() == 3) • { • (*node).nodeId = 'd'; • (*node).nodeArray[1] = 4; • (*node).nodeArray[4] = 3; • } • if (get_penum() == 4) • { • (*node).nodeId = 'e'; • (*node).nodeArray[1] = 3; • (*node).nodeArray[2] = 6; • (*node).nodeArray[3] = 3; • } • if (get_penum() == 5) • { • (*node).nodeId = 'f'; • (*node).nodeArray[2] = 9; • } • } //initilize

  24. MST in Cn By Hassan AL-Maksousy • // All processors whose distance d from their node to //root node is finite do • if ((node.nodeArray[root] >= 0)&& • (node.nodeArray[root] != 32)) • { • //Set their candidate$ field to 'yes' • node.candidate = 'y'; • //Set their parent$ field to root. • node.parent = root; • //Set current_best$ = d • node.current_best=node.nodeArray[root]; • } • //While the candidate field of some processor is 'yes' • while (control < 6 ) • { • //Restrict the active processors to those whose //candidate field • //is 'yes' and (for these processors) do • if (node.candidate == 'y') • { • mask = 1; • //Compute the minimum value x of current_best$. • minimum = min_int(node.current_best); • } • poly struct nodes node; • poly int nextNode; • int control=0; • int i; • poly int minCpu=100; • poly char letter[6]={'a','b','c','d','e','f'}; • if ( get_penum() < 6 ) • { • //All processors set • //candidate$ to 'wait' • //current-best$ to infinit • initialize(&node); • showNodes(node); • //the candidate field for the root node to 'no' • if (get_penum() == root) • { • node.candidate = 'n'; • control+=1; • printfp("Root = %c\n", letter[root]); • }

  25. MST in Cn By Hassan AL-Maksousy • if(node.candidate != 'n') • { • //If the value z in the next_node column of a //processor is less than • //its current_best$ value, then • if (node.nodeArray[nextNode] < node.current_best) • { • //Set current_best$ to z. • node.current_best = node.nodeArray[nextNode]; • //Set parent$ to next_node • node.parent = nextNode; • } • //For all processors, if candidate$ is "waiting" and //the distance of its • //node from next_node y is finite, then • if ((node.nodeArray[nextNode] < 32) && • (node.candidate == 'w')) • { • //Set candidate$ to "yes" • node.candidate = 'y'; • nextNode = -1; • showNodes(node); • //Restrict the active processors to those with //current_best$ = x and do • if ((mask == 1) && • (minimum == node.current_best)) • { • minCpu=get_penum(); • minCpu=min_int(minCpu); • } • //pick an active processor, say node y • if ( minCpu == get_penum()) • { • //Set the candidate$ value of node y to 'no' • node.candidate = 'n'; • control+=1; • nextNode = get_penum(); • printfp("Next Node = %c\n", letter[nextNode]); • } • // save nextNode value to all processor • nextNode = max_int(nextNode);

  26. MST in Cn By Hassan AL-Maksousy • Node a: Candidate w, Parent: , Current Best: 0 • Node b: Candidate w, Parent: , Current Best: 0 • Node c: Candidate w, Parent: , Current Best: 0 • Node d: Candidate w, Parent: , Current Best: 0 • Node e: Candidate w, Parent: , Current Best: 0 • Node f: Candidate w, Parent: , Current Best: 0 • Root = a • Node a: Candidate n, Parent: , Current Best: 0 • Node b: Candidate y, Parent: a, Current Best: 2 • Node c: Candidate y, Parent: a, Current Best: 8 • Node d: Candidate w, Parent: , Current Best: 0 • Node e: Candidate w, Parent: , Current Best: 0 • Node f: Candidate w, Parent: , Current Best: 0 • Next Node = b • Node a: Candidate n, Parent: , Current Best: 0 • Node b: Candidate n, Parent: a, Current Best: 2 • Node c: Candidate y, Parent: b, Current Best: 7 • Node d: Candidate y, Parent: b, Current Best: 4 • Node e: Candidate y, Parent: b, Current Best: 3 • Node f: Candidate w, Parent: , Current Best: 0 • //Set current_best$ to the distance of its node from y. • node.current_best = node.nodeArray[nextNode]; • //Set parent$ to y. • node.parent = nextNode; • } • } // endif 'n' • mask = 0; • minCpu = 100 ; • } //end while • showNodes(node); • printf ("End of program \n"); • }//endifget_penum() • } //main • // Compiling and running the program • -bash-3.00$ csreset • -bash-3.00$ cscn asc.cn mst.cn • -bash-3.00$ csruna.csx

  27. MST in Cn By Hassan AL-Maksousy Next Node = f Node a: Candidate n, Parent: , Current Best: 0 Node b: Candidate n, Parent: a, Current Best: 2 Node c: Candidate n, Parent: e, Current Best: 6 Node d: Candidate n, Parent: e, Current Best: 3 Node e: Candidate n, Parent: b, Current Best: 3 Node f: Candidate n, Parent: c, Current Best: 9 End of program Next Node = e Node a: Candidate n, Parent: , Current Best: 0 Node b: Candidate n, Parent: a, Current Best: 2 Node c: Candidate y, Parent: e, Current Best: 6 Node d: Candidate y, Parent: e, Current Best: 3 Node e: Candidate n, Parent: b, Current Best: 3 Node f: Candidate w, Parent: , Current Best: 0 Next Node = d Node a: Candidate n, Parent: , Current Best: 0 Node b: Candidate n, Parent: a, Current Best: 2 Node c: Candidate y, Parent: e, Current Best: 6 Node d: Candidate n, Parent: e, Current Best: 3 Node e: Candidate n, Parent: b, Current Best: 3 Node f: Candidate w, Parent: , Current Best: 0 Next Node = c Node a: Candidate n, Parent: , Current Best: 0 Node b: Candidate n, Parent: a, Current Best: 2 Node c: Candidate n, Parent: e, Current Best: 6 Node d: Candidate n, Parent: e, Current Best: 3 Node e: Candidate n, Parent: b, Current Best: 3 Node f: Candidate y, Parent: c, Current Best: 9

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