Abstract
We present a deterministic algorithm for selecting the element of rank k among N=n2 elements, 1≤k≤N, on an n×n mesh-connected processor array in (1.44+ε parallel computation steps, for any constant ε>0, using constant sized queues. This is a considerable improvement over the best previous deterministic algorithm, which was based upon sorting and required 3n steps. Our algorithm can be generalized to solve the problem of selection on higher dimensional meshes, achieving time bounds better than the known results in each case.
Preview
Unable to display preview. Download preview PDF.
References
M. Ajtai, N. Komlos, W. L. Steiger, and E. Szemeredi. Optimal parallel selection has complexity o(loglogn). Journal of Computer and System Science, 38(1):125–133, February 1989.
Y. Azar and N. Pippenger. Parallel selection. Discrete Applied Mathematics, 27:49–58, 1990.
M. Blum, R. Floyd, V. R. Pratt, R. Rivest, and R. Tarjan. Time bounds for selection. Journal of Computer and System Science, 7(4):448–461, 1972.
R. Cole. An optimally efficient selection algorithm. Information Processing Letters, 26:295–299, 1988.
R. Cypher and G. Plaxton. Deterministic sorting in nearly logarithmic time on the hypercube and related computers. In Symposium on the Theory of Computation, pages 193–203, 1990.
C. Kaklamanis, D. Krizanc, L. Narayanan, and A. Tsantilas. Randomized sorting and selection on mesh-connected processor arrays. In Symposium on Parallel Algorithms and Architecture, pages 17–28, 1991.
M. Kunde. Routing and sorting on mesh-connected arrays. In Aegean Workshop on Computing: VLSI algorithms and architectures. Vol.319 of Lecture Notes in Computer Science, Springer Verlag, NY, pages 423–433, 1988.
M. Kunde. 1-selection and related problems on grids of processors. Technical report, Institut fur Informatik, Technische Universitat, Munchen, 1989.
F.T. Leighton, F. Makedon, and I. Tollis. A 2n-2 step algorithm for routing in an n×n array with constant size queues. In Symposium on Parallel Algorithms and Architecture, pages 328–335, 1989.
F. Makedon and A. Simvonis. Many-to-one packet routing for the mesh. Technical report, University of Texas at Dallas, 1991.
G. Plaxton. Load balancing, selection and sorting on the hypercube. In Symposium on Parallel Algorithms and Architecture, pages 64–73. ACM, 1989.
G. Plaxton. On the network complexity of selection. In Symposium on the Foundations of Computer Science, pages 396–401. IEEE, 1989.
R. Reischuk. Probabilistic parallel algorithms for sorting and selection. SIAM Journal of Computing, 14(2):396–411, May 1985.
S. Rajasekaran and T. Tsantilas. Optimal algorithms for routing on the mesh. Algorithmica. to appear.
C. Schnorr and A. Shamir. An optimal sorting algorithm for mesh connected computers. In Symposium on the Theory of Computation, pages 255–263, 1986.
C. Thompson and H. Kung. Sorting on a mesh connected parallel computer. Communications of the ACM, 20:263–270, 1977.
L. Valiant. Parallelism in comparison problems. SIAM Journal of Computing, 4:348–355, 1975.
U. Vishkin. An optimal parallel algorithm for selection. In Advances in Computing Research, pages 79–85. Jai Press, inc., 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krizanc, D., Narayanan, L., Raman, R. (1991). Fast deterministic selection on mesh-connected processor arrays. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_79
Download citation
DOI: https://doi.org/10.1007/3-540-54967-6_79
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54967-3
Online ISBN: 978-3-540-46612-3
eBook Packages: Springer Book Archive