Parallel Algorithms for Routing in Nonblocking Networks

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Mathematics (HMC)

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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 with n inputs and n outputs have size O(n(logn)2) and depth O(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 uses O((logn)5) steps to process any number of transactions in parallel (with one processor per transaction), maintaining a data structure that use O(n(logn)2) words.

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© 1994 Springer-Verlag New York Inc.

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