This Article 
 Bibliographic References 
 Add to: 
On Balancing Sorting on a Linear Array
May 1993 (vol. 4 no. 5)
pp. 566-571

A balanced parallel algorithm to sort a sequence of items on a linear array of processors is presented. The length of the sequence may be small to arbitrarily large. For a shortsequence, the output of the sorted sequence begins at the step following the last inputof the whole sequence. For an arbitrarily long sequence, the time complexity is optimalunder realistic hardware conditions. A variation of the algorithm is also introduced. Bothalgorithms require far less local memory than that required by a different approach ofbalanced computation. Any number of balanced processors can be connected to delivermore computing power without increasing the memory size of each processor.

[1] S. G. Akl,Parallel Sorting Algorithms. Orlando, FL: Academic, 1985.
[2] Selim G. Akl,The Design and Analysis of Parallel Algorithms. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[3] S. G. Akl and H. Schmeck, "Systolic sorting in a sequential input/output environment,"Parallel Comput., vol. 3, pp. 11-23, 1986.
[4] Inmos,Occam 2 Reference Manual. New York: Prentice-Hall, 1988.
[5] Inmos,The Transputer Databook. Almondsbury, Bristol, UK: Inmos, 1989.
[6] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.
[7] H. T. Kung, "Memory requirements for balanced computation,"J. Complexity, vol. 1, pp. 147-157, 1985.
[8] D. T. Lee, H. Chang, and C. K. Wong, "An on-chip compare/steer bubble sorter,"IEEE Trans. Comput., vol. C-30, pp. 396-405, June 1981.
[9] C. E. Leiserson, "Systolic priority queues," Tech. Rep. No. CMU-CS-79- 115, Dept. Comput. Sci., Carnegie-Mellon Univ., Pittsburgh, PA, Apr. 1979.
[10] F. C. Lin and J. C. Shieh, "Space and time complexities of balanced sorting on processor arrays,"J. Complexity, vol. 6, pp. 365-378, 1990.
[11] G. Miranker, L. Tang, and C. K. Wong, "A 'zero-time' VLSI sorter,"IBM J. Res. Develop., vol. 27, pp. 140-148, Mar. 1983.
[12] A. Park and K. Balasubramanian, "Reducing communication costs for sorting on mesh-connected and linearly connected parallel computers,"J. Parallel and Distributed Comput., vol. 9, pp. 318-322, 1990.
[13] M. Quinn,Designing Efficient Algorithms for Parallel Computers. New York: McGraw-Hill, 1987.

Index Terms:
Index Termsbalanced parallel algorithm; linear array; local memory; balanced computation; computational complexity; parallel algorithms; sorting
Y.C. Lin, "On Balancing Sorting on a Linear Array," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 5, pp. 566-571, May 1993, doi:10.1109/71.224219
Usage of this product signifies your acceptance of the Terms of Use.