Randomized routing on meshes with buses

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Abstract

We give algorithms and lower bounds for the problem of routing k-permututions on d-dimensional MIMD meshes with row and column Buses We prove a lower bound for routing permutations (the case k = 1) on d-dimensional meshes. For d = 2, 3 and 4 the lower bound is respectivdy 0.69 · n, 0.72 · n and 0.76 · 9 steps; the bound increases monotonically with d and is at least (1 - 1/d) · n steps for all d ≥ 5. Previously, u bisection argument had been used to show that for all d ≥ 1, 0.66 · n steps are required for this problem (i.e., the lower bound did not increase with increasing d). These lower bounds hold for off-line routing as well. We give a general algorithm that routes k-permutations on d-dimensional meshes in min{(2 - 1/d) · k · n, max{4/3 · d · n,k · n/3}} + o(d · k · n) steps, for all k,d ≥ 1. This improves considerably on previous results for many values of Ir and d. In pastlculaz, the routing time for permutations is bounded by 2 · 9n, for all 1 ≤ d

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Sibeyn, J. F., Kaufmann, M., & Raman, R. (1993). Randomized routing on meshes with buses. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 726 LNCS, pp. 333–344). Springer Verlag. https://doi.org/10.1007/3-540-57273-2_68

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