(k minus k) routing on multidimensional mesh-connected arrays

Journal Article · Fri Feb 01 04:00:00 EST 1991 · Journal of Parallel and Distributed Computing; (United States)

DOI:https://doi.org/10.1016/0743-7315(91)90120-X· OSTI ID:5070764

Kunde, M; Tensi, T ^[1]

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1. Inst. fuer Informatik, Technische Univ., Muenchen, Arcisstrasse 21, D-8000 Muechen 2 (DE)

In this paper the authors study the problem of routing packets on an r-dimensional mesh-connected array of processors. The focus of this paper is on routing with each processor containing exactly k packets, k {ge} 2, initially and finally (so-called k-k routing). For two- dimensional n {times} n grids the number of transport steps is at most 5/4 kn + O(kn/f(n)) with a buffer size of O(kf(n)). In the special case of a sequence of k permutation routing problems this step count can be reduced to kn + O(kn/f(n)). For an r-dimensional grid, r {ge} 3, with side length n the same technique yields an algorithm with step count (r {minus} 1)(1 + 1/r{sup 2})kn + O(n/f(n){sup 1/(r{minus}1)}) and a buffer rk {center dot} f(n). For sequences of permutation routing problems this drops to (k/r) (2r {minus} 2)n + O(kn/f(n){sup 1/(r{minus}1)}) and a buffer size of O(kf(n)). Furthermore it is shown that splitting large packets into smaller ones has benefits for permutation routing problems. For grids with wraparound connections these step counts and times generally can be reduced by one-half.

• OSTI ID: 5070764
• Journal Information: Journal of Parallel and Distributed Computing; (United States), Journal Name: Journal of Parallel and Distributed Computing; (United States) Vol. 11:2; ISSN JPDCE; ISSN 0743-7315
• Country of Publication: United States
• Language: English

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