Abstract
A sequential random access machine can permute n data items in n steps. However, Gottlieb and Kruskal have shown that any bounded degree machine with P processors requires Ω((n/P) log P) time to permute n data items and this result makes the issue of optimal speedup interesting for interconnection networks. In this paper, we consider the issue of optimal speedup for sorting and graph problems and provide the following results: (1) If a network with P processors can permute P elements in O(log P) time, then n data items can be sorted on this network in Θ((n/P) log n) time when n≥P 1+ɛ. An important consequence of this result is that a single step of any Concurrent Read Concurrent Write PRAM (CRCW-PRAM) algorithm that uses n processors and O(n) memory space, can be simulated optimally (when n≥P 1+ɛ) by any network with P processors that can permute P data items in O(log P) time. (2) The connected components, biconnected components, and the minimum spanning forest can be determined in optimal time for any network that has P processors as long as P ≤ n 2 / log2 n and as long as this network can perform a restrictive set of permutations of P items in O(log P) time. Our paradigm for solving graph problems is quite general and it can be extended to optimally compute the median of n numbers on interconnection networks.
This work was done when the author was visiting IBM Thomas J. Watson Research Center in 1984–85.
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© 1988 Springer-Verlag Berlin Heidelberg
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Aggarwal, A., Huang, MD.A. (1988). Network complexity of sorting and graph problems and simulating CRCW PRAMS by interconnection networks. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040401
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DOI: https://doi.org/10.1007/BFb0040401
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