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Parallel algorithms for routing in nonblocking networks

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Abstract

We construct nonblocking networks that are efficient not only as regards their cost and delay, but also as regards the time and space required to control them. In this paper we present the first simultaneous “weakly optimal” solutions for the explicit construction of nonblocking networks, the design of algorithms and data-structures. “Weakly optimal” is in the sense that all measures of complexity (size and depth of the network, time for the algorithm, space for the data-structure, and number of processor-time product) are within one or more logarithmic factors of their smallest possible values. In fact, we construct a scheme in which networks withn inputs andn outputs have sizeO(n(logn)2) and depthO(logn), and we present deterministic and randomized on-line parallel algorithms to establish and abolish routes dynamically in these networks. In particular, the deterministic algorithm usesO((logn)5) steps to process any number of transactions in parallel (with one processor per transaction), maintaining a data structure that useO(n(logn)2) words.

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Authors and Affiliations

  1. Department of Computer Science, The University of British Columbia, V6T 1Z2, Vancouver, British Columbia, Canada

    Geng Lin & Nicholas Pippenger

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  1. Geng Lin
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  2. Nicholas Pippenger
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Lin, G., Pippenger, N. Parallel algorithms for routing in nonblocking networks. Math. Systems Theory 27, 29–40 (1994). https://doi.org/10.1007/BF01187091

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  • DOI: https://doi.org/10.1007/BF01187091

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