Abstract
We show that there is a randomized oblivious algorithm for routing any (partial) permutation on an n × n grid in 2n+O (log n) parallel communication steps. The queues will not grow larger than Θ(log n) with high probability. We then modify this to obtain a (non-oblivious) algorithm with the same running time such that the size of the queues is bounded by a constant with high probability. For permutations with locality, where each packet has to travel distance at most L in either the horizontal or the vertical direction, a generalization of the algorithm routes in time 3L+o(L), while the queue size remains bounded by Θ(log n) with high probability. Finally, we show that for a general class of oblivious deterministic routing strategies, Ω(n 2) time is required if we want to have constant size queues.
Supported in part by NSF Grant NSF-DCR-86-00379 and by an NSERC Postgraduate Scholarship
Supported in part by NSF Grant NSF-DCR-85-03251 and ONR contract N00014-80-C-0647
Supported in part by NSF Grant NSF-DCR-86-00379
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Krizanc, D., Rajasekaran, S., Tsantilas, T. (1988). Optimal routing algorithms for mesh-connected processor arrays. 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/BFb0040408
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DOI: https://doi.org/10.1007/BFb0040408
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