Fast deterministic selection on mesh-connected processor arrays
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.
KeywordsParallel Algorithm Deterministic Algorithm Sorting Algorithm Sample Element Corner Vertex
Unable to display preview. Download preview PDF.
- [BFP+72]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.Google Scholar
- [CP90]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.Google Scholar
- [KKNT91]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.Google Scholar
- [Kun88]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.Google Scholar
- [Kun89]M. Kunde. 1-selection and related problems on grids of processors. Technical report, Institut fur Informatik, Technische Universitat, Munchen, 1989.Google Scholar
- [LMT89]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.Google Scholar
- [MS91]F. Makedon and A. Simvonis. Many-to-one packet routing for the mesh. Technical report, University of Texas at Dallas, 1991.Google Scholar
- [Pla89a]G. Plaxton. Load balancing, selection and sorting on the hypercube. In Symposium on Parallel Algorithms and Architecture, pages 64–73. ACM, 1989.Google Scholar
- [Pla89b]G. Plaxton. On the network complexity of selection. In Symposium on the Foundations of Computer Science, pages 396–401. IEEE, 1989.Google Scholar
- [RT]S. Rajasekaran and T. Tsantilas. Optimal algorithms for routing on the mesh. Algorithmica. to appear.Google Scholar
- [SS86]C. Schnorr and A. Shamir. An optimal sorting algorithm for mesh connected computers. In Symposium on the Theory of Computation, pages 255–263, 1986.Google Scholar
- [Vis87]U. Vishkin. An optimal parallel algorithm for selection. In Advances in Computing Research, pages 79–85. Jai Press, inc., 1987.Google Scholar