This describes a new parallel sorting algorithm suitable for a variety of multiprocessor architectures. Parallel Sorting by Regular Sampling (PSRS) finds pivots for partitioning the data into ordered subsets of approximately equal size by using a regular sample from sorted sublists of the data.

1. Parallel Sorting by
Regular Sampling
muwei@cn.ibm.com
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2. Speedup of Parallel
Sort
• Average memory latency
• Overhead of scheduling and
synchronization
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3. Traditional Parallel Sort
Most 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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4. 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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5. 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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6. PSRS
• Data distribution is unkown
• Find pivots for partitioning data
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7. 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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8. 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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9. 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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10. PSRS Example
16 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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11. Complexity Analysis
• Phase 1
• Phase 2
• Phase 3
Complexity for PSRS is :
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12. Q & A
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