Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
How much can hardware help routing?
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A d-move local permutation routing for the d-cube
Discrete Applied Mathematics
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Graphs partitioning: an optimal MIMD queueless routing for BPC-permutations on hypercubes
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
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Oblivious permutation routing in binary d-cubes has been well studied in the literature. In a permutation routing, each node initially contains a packet with a destination such that all the 2d destinations are distinct. Kaklamanis et al. (Math. Syst. Theory 24 (1991) 223-232) used the decomposability of hypercubes into Hamiltonian circuits to give an asymptotically optimal routing algorithm. The notion of "destination graph" was first introduced by Borodin and Hopcroft to derive lower bounds on routing algorithms. This idea was recently used by Grammatikakis et al. (Proceedings of the Advancement in Parallel Computing, Elsevier, Amsterdam, 1993) to construct many-one routing algorithms for the binary 2-cube and 3-cube. In the present paper, further theoretical development is made along this line. It is then applied to obtain algorithms for binary d-cubes with d up to 12, which compare favorably with the above-mentioned "Hamiltonian circuit" algorithm. Some results on t-nary cubes with t≥3 are also obtained.