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Practical Algorithms for Selection on Coarse-Grained Parallel Computers
August 1997 (vol. 8 no. 8)
pp. 813-824

Abstract—In this paper, we consider the problem of selection on coarse-grained distributed memory parallel computers. We discuss several deterministic and randomized algorithms for parallel selection. We also consider several algorithms for load balancing needed to keep a balanced distribution of data across processors during the execution of the selection algorithms. We have carried out detailed implementations of all the algorithms discussed on the CM-5 and report on the experimental results. The results clearly demonstrate the role of randomization in reducing communication overhead.

[1] M. Ajtai, J. Komlo's, W.L. Steiger, and E. Szemere'di, "Deterministic Selection in O(log log N) Parallel Time," Proc. 18th Ann. ACM Symp. n Theory of Computing, pp. 188-195, 1986.
[2] S.G. Akl, The Design and Analysis of Parallel Algorithms. Orlando, Fl.: Academic Press, 1989.
[3] S.G. Akl, "Parallel Selection in O(log log n) Time Using O(n/log log n) Processors," Technical Report 88-221, Dept. of Computing and Information Science, Queen's Univ., Kingston, Ontario, Mar. 1988.
[4] S.G. Akl, "An Optimal Algorithm for Parallel Selection," Information Processing Letters, vol. 19, no. 1, pp. 47-50, 1984.
[5] D.A. Bader and J. J'aJ'a, "Practical Parallel Algorithms for Dynamic Data Redistribution, Median Finding and Selection," Technical Report CS-TR-3494, School of Computer Science, Univ. of Maryland, July 1995.
[6] Berthomi, A. Ferreira, B.M. Maggs, S. Perennes, and C.G. Plaxton, "Sorting-Based Selection Algorithms for Hypercubic Networks," Proc. Seventh Int'l Parallel Processing Symp., pp. 89-95, 1993.
[7] G.E. Blelloch, "Prefix Sums and Their Applications," Technical Report CMU-CS-90-190, School of Computer Science, Carnegie Mellon Univ., Nov. 1990.
[8] M. Blum, R.W. Floyd, V.R. Pratt, R.L. Rivest, and R.E. Tarjan, "Time Bounds for Selection," J. Computer and System Sciences, vol. 7, no. 4, pp. 448-461, 1972.
[9] R. Cole and C.K. Yap, "A Parallel Median Algorithm," Information Processing Letters, vol. 20, no. 3, pp. 137-139, 1985.
[10] T.H. Cormen,C.E. Leiserson, and R.L. Rivest,Introduction to Algorithms.Cambridge, Mass.: MIT Press/McGraw-Hill, 1990.
[11] G. Cybenko, "Dynamic Load Balancing for Distributed Memory Multiprocessors," J. Parallel and Distributed Computing, vol. 7, pp. 279-301, 1989.
[12] R.W. Floyd and R.L. Rivest, "Expected Time Bounds for Selection," Comm. ACM, vol. 18, no. 3, pp. 165-172, 1975.
[13] E. Hao, P.D. MacLenzie, and Q.F. Stout, "Selection on the Reconfigurable Mesh," Proc. Fourth Symp. Frontiers of Massively Parallel Computation, pp. 38-45, 1992.
[14] J. J'aJ'a, An Introduction to Parallel Algorithms.New York: Addison-Wesley, 1992.
[15] V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin Cummings, 1994.
[16] C.G. Plaxton, "Efficient Computation on Sparse Interconnection Networks," PhD thesis, Dept. of Computer Science, Stanford Univ., 1989.
[17] S. Rajasekharan, W. Chen, and S. Yooseph, "Unifying Themes for Parallel Selection," Proc. Fifth Int'l Symp. Algorithms and Computation, Springer-Verlag Lecture Notes in Computer Science 834, pp. 92-100,Beijing, China, 1994.
[18] S. Rajasekharan and J.H. Reif, "Derivation of Randomized Sorting and Selection Algorithms," Parallel Algorithm Derivation and Program Transformation, R. Paige, J.H. Reif, and R. Watcher, eds., pp. 187-205, Kluwer Academic, 1993.
[19] S. Rajasekharan, "Randomized Parallel Selection," Proc. Symp. Foundations of Software Technology and Theoretical Computer Science, pp. 215-224, 1990.
[20] S. Ranka, R.V. Shankar, and K.A. Alsabti, "Many-to-Many Communication with Bounded Traffic," Proc. Frontiers Massively Parallel Computation, pp. 20-27, 1995.
[21] S. Ranka, Y. Won, and S. Sahni, "Programming a Hypercube Multicomputer," IEEE Software, pp. 69-77, Sept. 1988.
[22] R. Sarnath and X. He, "Efficient Parallel Algorithms for Selection and Searching on Sorted Matrices," Proc. Sixth Int'l Parallel Processing Symp., pp. 108-111, 1992.
[23] A. Schonhage, M.S. Paterson, and N. Pippenger, "Finding the Median," J. Computer and System Sciences, vol. 13, pp. 184-199, 1976.
[24] R.V. Shankar and S. Ranka, "Random Data Accesses on a Coarse-Grained Parallel Machine II: One-to-Many and Many-to-One Mappings," CIS technical report, Syracuse Univ., 1994.
[25] J. Woo and S. Sahni, "Load Balancing on a Hypercube," Proc. Fifth Int'l Parallel Processing Symp., pp. 525-530, 1991.

Index Terms:
Coarse-grained, hypercubes, load balancing, median finding, meshes, randomized algorithms, selection, parallel algorithms, parallel computers.
Ibraheem Al-furiah, Srinivas Aluru, Sanjay Goil, Sanjay Ranka, "Practical Algorithms for Selection on Coarse-Grained Parallel Computers," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 8, pp. 813-824, Aug. 1997, doi:10.1109/71.605768
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