This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Sorting in Mesh Connected Multiprocessors
September 1992 (vol. 3 no. 5)
pp. 626-632
A sorting algorithm, dubbed MeshSort, for multidimensional mesh-connected multiprocessors is introduced. Bitonic Sort and ShearSort are shown to be special cases of MeshSort. MeshSort thus provides some insight into the operation of parallel sorting. It requires operations only along orthogonal vectors of processors, simplifying the control of the multiprocessor. This allows MeshSort to be used on any reduced architecture where a multidimensional memory structure is interconnected with a lower dimensional structure of processors. A modified version of MeshSort, called FastMeshSort, is presented. This algorithm applies the same basic principle as MeshSort, and is almost as simple to implement, but achieves much better performance. The modified algorithm is shown to be very efficient for reasonably sized meshes. FastMeshSort is presented as a practical sorting and routing algorithm for real multidimensional mesh-connected multiprocessors. The algorithms can easily be extended to other multiprocessor structures.

[1] S. G. Akl,Parallel Sorting Algorithms. Orlando, FL: Academic, 1985.
[2] K. E. Batcher, "Sorting networks and their applications," inProc. AFIPS Conf. Proc., 1968 Spring Joint Comput. Conf., 1968, pp. 307-314.
[3] G. Baudet and D. Stevenson, "Optimal sorting algorithms for parallel computers,"IEEE Trans. Comput., vol. C-27, no. 1, pp. 84-87, Jan. 1978.
[4] R. Cypher and C. G. Plaxton, "Deterministic sorting in nearly logarithmic time on the hypercube and related computers," inProc. 22nd ACM Symp. Theory Comput., 1990, pp. 193-203.
[5] R. Cypher and J. L. C. Sanz, "Optimal sorting on reduced architectures," inProc. Int. Conf. Parallel Processing, vol. 3, St. Charles, IL, Aug. 1988, pp. 308-311.
[6] Y. Han and Y. Igarashi, "Time lower bounds for sorting on multi-dimensional mesh-connected processor arrays," inProc. Int. Conf. Parallel Processing, vol. 3, St. Charles, IL, Aug. 1988, pp. 194-197.
[7] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.
[8] M. Kunde, "Lower bounds for sorting on mesh-connected architectures," inProc. VLSI Algorithms and Architectures: Aegean Workshop Comput., June 1986, pp. 84-95.
[9] M. Kunde, "Optimal sorting on multi-dimensionally mesh-connected computers," inProc. Symp. Theoret. Aspects Comput. Sci., Feb. 1987, pp. 408-419.
[10] T. Leighton, "Tight bounds on the complexity of parallel sorting,"IEEE Trans. Comput., vol. C-34, no. 4, pp. 344-354, Apr. 1985.
[11] J. M. Marberg and E. Gafni, "Sorting in constant number of row and column phases on a mesh," inProc. 24th Annu. Allerton Conf. Commun., Contr., Comput., Oct. 1986, pp. 603-612.
[12] D. Nassimi and S. Sahni, "Bitonic sort on a mesh-connected parallel computer,"IEEE Trans. Comput., vol. C-27, no. 1, pp. 2-7, Jan. 1979.
[13] G. Plaxton, "Load balancing, selection and sorting on the hypercube," inProc. 1st ACM Symp. Parallel Algorithms and Architectures, June 1989, pp. 64-73.
[14] L. Rudolph, "A robust sorting network,"IEEE Trans. Comput., vol. C-34, no. 4, pp. 326-335, Apr. 1985.
[15] K. Sado and Y. Igarashi, "Some parallel sorts on a mesh-connected processor array and their time efficiency,"J. Parallel Distributed Comput., vol. 3, pp. 398-410, Sept. 1986.
[16] I. D. Scherson, "Orthogonal graphs for the construction of a class of interconnection networks,"IEEE Trans. Parallel Distributed Syst., vol. 2, no. 1, pp. 3-19, Jan. 1991.
[17] I. D. Scherson and Y. Ma, "Analysis and applications of an orthogonal access multiprocessor,"J. Parallel Distributed Comput., vol. 7, pp. 232-255, 1989.
[18] I. D. Scherson and S. Sen, "Parallel sorting in two-dimensional VLSI models of computation,"IEEE Trans. Comput., vol. 38, no. 2, pp. 238-249, Feb. 1989.
[19] I. D. Scherson, S. Sen, and A. Shamir, "Shearsort: A true two-dimensional sorting technique for VLSI networks," inProc. Int. Conf. Parallel Processing, 1986.
[20] C. P. Schnorr and A. Shamir, "An optimal sorting algorithm for mesh connected computers," inProc. 18th ACM Symp. Theory Comput., May 1986.
[21] H. S. Stone, "Parallel processing with the perfect shuffle,"IEEE Trans. Comput., vol. C-20, no. 2, pp. 153-161, Feb. 1971.
[22] C. D. Thompson and H. T. Kung, "Sorting on a mesh connected processor array,"Commun. ACM, pp. 263-271, 1972.

Index Terms:
Index Termssorting algorithm; MeshSort; multidimensional mesh-connected multiprocessors; Bitonic Sort; ShearSort; parallel sorting; orthogonal vectors; reduced architecture; multidimensional memory structure; FastMeshSort; routing algorithm; multiprocessor interconnection networks; parallel algorithms; sorting
Citation:
P.F. Corbett, I.D. Scherson, "Sorting in Mesh Connected Multiprocessors," IEEE Transactions on Parallel and Distributed Systems, vol. 3, no. 5, pp. 626-632, Sept. 1992, doi:10.1109/71.159046
Usage of this product signifies your acceptance of the Terms of Use.