A Comparison of Parallel Sorting Algorithms on
Different Architectures
Nancy M. Amato, Ravishankar Iyer, Sharad Sundaresan and Yan Wu
Texas A&M University
Hoang Bui
CMPS 5443
Overview





Introduction
Machine Descriptions
Parallel Sorting Algorithms
Experimental Results
Comparisons and Recommendations
Introduction




Sorting is one of the fundamental problems.
Sequential sorting and Parallel sorting.
Variety of parallel architectures.
Experimental study of three algorithms:


Bitonic sort, sample sort & parallel radix sort.
Apply to three different machines.
Machine Descriptions



The MasPar MP1201.
The nCUBE 2.
The Sequent Balance.
The MasPar MP1201





SIMD machine.
2,048 processors, 1.8 MIPS, 16Kbytes RAM.
Mesh based architecture.
X-Net and Global Router for communication.
Programming languages: C-Like and Fortran.
The nCUBE 2





MIMD machine.
64 processors, 7.5 MIPS 1Mbyte RAM.
Hypercube architecture.
Broadcasting.
Language: C.
The Sequent Balance





MIMD.
Shared Memory
10 processors, 8 Kbytes RAM.
Communicate through shared memory.
Running Unix, language: C.
Parallel Sorting Algorithms



Bitonic Sort.
Sample Sort.
Parallel Radix Sort.
Bitonic Sort

Bitonic Sequence:



Is the concatenation of an ascending and
descending sequence of numbers.
Example: 2,4,6,8,9,24,6,3,2,0.
Algorithm:


Convert n numbers into a bitonic sequence with
n/2 numbers in an increasing subsequence.
Merge into an ordered sequence (increasing or
decreasing.)
Sample sort

Algorithm:



Select p-1 splitters  p buckets.
Each number is put into the appropriate bucket.
Sort each buckets.
Parallel Radix Sort

Example list:


170, 45, 75, 90, 2, 24, 802, 66
Algorithm:



sorting by least significant digit (1s place) gives:
170, 90, 2, 802, 24, 45, 75, 66.
sorting by next digit (10s place) gives:
2, 802, 24, 45, 66, 170, 75, 90 .
sorting by most significant digit (100s place) gives:
2, 24, 45, 66, 75, 90, 170, 802
Experimental Results




Make modifications to each machine.
Code was written in C.
Keys are randomly generated 32 bit integers.
Repeat 25 times and calculate the average.
The MasPar MP1202 – Bitonic sort

Good speed-ups for all input size.
The MasPar MP1202 – Sample sort

Also good speed-ups.
The MasPar MP1202 – Radix sort

Shortest time for the MasPar MP1202.
The MasPar MP1202

Comparisons:
The nCUBE 2 – Bitonic Sort
The nCUBE 2 – Sample Sort
The nCUBE 2 – Radix Sort
The nCUBE 2
The Sequent Balance – Bitonic sort
The Sequent Balance – Sample sort
The Sequent Balance – Radix sort
The Sequent Balance
Comparisons and Recommendations

MasPar MP1202:



nCUBBE 2:


Bitonic Sort for smaller input size.
Parallel Radix Sort for larger input size.
Sample Sort is the best.
Sequent Balance:


Sample Sort for smaller input size.
Parallel Radix Sort for larger input size.
Question