parallel sorting by regular sampling
TRANSCRIPT
Parallel Sorting by Regular Sampling
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Speedup of Parallel Sort
• Average memory latency
• Overhead of scheduling and synchronization
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Traditional Parallel SortMost parallel sorts suitable for multiprocessor computers can be placed into one of two rough categories:
• Merge-based sorts
• Partition-based sorts
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Merge-based sorts
• Consist of multiple merge stages across processors, and perform well only with a small number of processors
• More larger the number of processors utilized gets , more larger the overhead of scheduling and synchronization hit
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Partition-based sorts
• Partitioning the data set into smaller subsets such that all elements in one subset are no greater than any element in another
• Sorting each subset in parallel
• The performance of partition-based sorts primarily depends on how well the data can be evenly partitioned into smaller ordered subsets
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PSRS
• Data distribution is unkown
• Find pivots for partitioning data
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PSRS：Phase 1• Each of p processors sorts a contiguous list
of size w=n/p using sequential Quicksort
• Define the regular sample of the locally ordered X be a set of the following p(p - 1 ) elements
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PSRS：Phase 2• Regular sample set, Y, is sorted using
sequential Quicksort
• Choose （p-1） pivots for partitioning X
• Each processor finds where each of the (p - 1) pivots divides its list, using a binary search.
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PSRS：Phase 3
• Each processor i performs a p-way Mergesort to merge all the i-th sorted sublists of p lists.
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PSRS Example16 2 17 24 33 28 30 1 0 27 9 25 34 23 19 18 11 7 21 13 8 35 12 29 6 3 4 14 22 15 32 10 26 31 20 5
0 1 2 9 16 17 24 25 27 28 30 33
7 8 11 12 13 18 19 21 23 29 34 35
3 4 5 6 10 14 15 20 22 26 31 32
0 1 2 9 16 17 24 25 27 28 30 33
7 8 11 12 13 18 19 21 23 29 34 35
3 4 5 6 10 14 15 20 22 26 31 32
1610 13 22 23 27
1610 13 22 23 27
0 1 2 9 7 8 3 4 5 6 10 16 17 11 12 13 18 19 21 14 15 20 22 24 25 27 28 30 33 23 29 34 35 26 31 32
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Complexity Analysis• Phase 1
• Phase 2
• Phase 3
Complexity for PSRS is :
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Q & A
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