11f6643lec13 - Floyd’s Algorithm Rajendra V Boppana...

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Unformatted text preview: Floyd’s Algorithm Rajendra V. Boppana Slides adapted from M.J. Quinn, Parallel Programming in C with MPI and OpenMP, McGraw Hill, 2004 CS6643 F'11 Lec13 1 Objectives •Creating 2-D arrays •Thinking about “grain size” •Point-to-point communications •Reading and printing 2-D matrices •Analyzing performance when computations and communications overlap CS6643 F'11 Lec13 2 Outline •All-pairs shortest path problem •Dynamic 2-D arrays •Parallel algorithm design •Point-to-point communication •Block row matrix I/O •Analysis and benchmarking CS6643 F'11 Lec13 3 All-pairs Shortest Path Problem CS6643 F'11 Lec13 4 A E B C D 4 6 1 3 5 3 1 2 6 3 6 4 7 10 12 6 3 7 3 10 9 5 12 2 A B C D E A B C D 4 8 1 11 E The adjacency matrix for the graph Floyd’s Algorithm CS6643 F'11 Lec13 5 for k g 0 to n-1 for i g 0 to n-1 for j g 0 to n-1 a[i,j] g min ( a[i,j] , a[i,k] + a[k,j] ) endfor endfor endfor Why It Works CS6643 F'11 Lec13 6 i k j Shortest path from i to k through 0, 1, …, k-1 Shortest path from k to j through 0, 1, …, k-1 Shortest path from i to j through 0, 1, …, k-1 Computed in previous iterations Dynamic 1-D Array Creation CS6643 F'11 Lec13 7 A Heap Run-time Stack Dynamic 2-D Array Creation CS6643 F'11 Lec13 8 Heap Run-time Stack Bstorage B Designing Parallel Algorithm •Partitioning •Communication •Agglomeration and Mapping CS6643 F'11 Lec13 9 Partitioning •Domain or functional decomposition? •Domain or functional decomposition?...
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This note was uploaded on 01/29/2012 for the course CS 6643 taught by Professor Staff during the Fall '08 term at The University of Texas at San Antonio- San Antonio.

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11f6643lec13 - Floyd’s Algorithm Rajendra V Boppana...

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