This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Parallel Divide and Conquer on Meshes
October 1996 (vol. 7 no. 10)
pp. 1049-1058

Abstract—We address the problem of mapping divide-and-conquer programs to mesh connected multicomputers with wormhole or store-and-forward routing. We propose the binomial tree as an efficient model of parallel divide-and-conquer and present two mappings of the binomial tree to the 2D mesh. Our mappings exploit regularity in the communication structure of the divide-and-conquer computation and are also sensitive to the underlying flow control scheme of the target architecture. We evaluate these mappings using new metrics which are extensions of the classical notions of dilation and contention. We introduce the notion of communication slowdown as a measure of the total communication overhead incurred by a parallel computation. We conclude that significant performance gains can be realized when the mapping is sensitive to the flow control scheme of the target architecture.

[1] A. Agarwal, "Limits on Network Performance," MIT VLSI memo, 1990.
[2] W.C. Athas and C.L. Seitz, “Multicomputers: Message-Passing Concurrent Computers,” Computer, vol. 21, pp. 9-24, Aug. 1988.
[3] G.E. Blelloch,Vector Models for Data-Parallel Computing. The MIT Press, 1990.
[4] S.H. Bokhari, Assignment Problems in Parallel and Distributed Computing.Boston: Kluwer Academic, 1987.
[5] S.H. Bokhari, "Communication Overhead on the Intel iPSC-860 Hypercube," technical report, ICASE, NASA Langley Research Center, May 1990.
[6] S.S. Chittor, "Communication Performance of Multicomputers," PhD thesis, Dept. of Computer Science, Michigan State Univ., 1991.
[7] M.I. Cole, Algorithmic Skeletons: Structured Management of Parallel Computation, MIT Press, Cambridge, Mass., 1989.
[8] W.J. Dally, "Performance Analysis of k-ary n-Cube Interconnection Networks," IEEE Trans. Computers, vol. 39, no. 6, pp. 775-785, June 1992.
[9] T.H. Dunigan, "Performance of the Intel iPSC/860 and Ncube 6400 Hypercubes," Parallel Computing, vol. 17, pp. 1,285-1,302, 1991.
[10] C.L. Seitz et al., "The Architecture and Programming of the Ametak Series 2010," Proc. Third Conf. Hypercube Concurrent Computers and Applications, pp. 33-37, Jan. 1988.
[11] S.L. Johnson, "Communication in Network Architectures," VLSI and Parallel Computation, p. 290, Morgan Kaufmann, 1990.
[12] P. Kermani and L. Kleinrock, "Virtual Cut-Through: A New Computer Communication Switching Technique," Computer Networks, vol. 3, pp. 267-286, 1979.
[13] Z.G. Mou and P. Hudak, "An Algebraic Model for Divide-and-Conquer Algorithms and its Parallelism," J. Supercomputing, vol. 2, no. 3, pp. 257-278, Nov. 1988.
[14] P.A. Nelson and L. Snyder, "Programming Paradigms for Nonshared Memory Parallel Computers," The Characteristics of Parallel Algorithms, pp. 3-20, MIT Press, 1987.
[15] A.L. Rosenberg, "Graph Embeddings 1988: Recent Breakthroughs New Directions," Technical Report No. 88-28, Univ. of Massachusetts at Amherst, Mar. 1988.
[16] H.S. Stone, "Multiprocessor Scheduling with the Aid of Network Flow Algorithms," IEEE Trans. Software Engineering, vol. 3, no. 1, pp. 85-93, Jan. 1977.
[17] J.D. Ullman, Computation Aspects of VLSI.Rockville, Md.: Computer Science Press, 1984.
[18] J. Vuillemin, "A Data Structure for Manipulating Priority Queues," Comm. ACM, vol. 21, no. 4, pp. 309-315, Apr. 1987.

Index Terms:
Mapping, embedding, divide-and-conquer algorithms, binomial tree, mesh connected machines, routing, wormhole routing, store-and-forward routing, contention, dilation.
Citation:
Virginia Lo, Sanjay Rajopadhye, Jan Arne Telle, Xiaoxiong Zhong, "Parallel Divide and Conquer on Meshes," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 10, pp. 1049-1058, Oct. 1996, doi:10.1109/71.539736
Usage of this product signifies your acceptance of the Terms of Use.