Optimal embeddings of multiple graphs into a hypermesh

  • Authors:
  • Sook-Yeon Kim;Kyung-Yong Chwa

  • Affiliations:
  • -;-

  • Venue:
  • ICPADS '97 Proceedings of the 1997 International Conference on Parallel and Distributed Systems
  • Year:
  • 1997

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Abstract

A hypermesh, a versatile parallel architecture, is obtained from a 2-dimensional mesh by replacing each linear connection with a hyper-edge. We optimally embed multiple graphs into a hypermesh by a labeling strategy. This optimal embedding provides an optimal expansion, dilation and congestion at the same time. First, we label on an N-node graph G, possibly disconnected, such that this labeling makes it possible to optimally embed multiple copies of G into an N'/spl times/N' hypermesh when N' is divisible by N. Second, we show that many important classes of graphs have this labeling: for example, tree, cycle, mesh of trees and product graphs including mesh, torus, and hypercube. Third, we generalize these results to optimally embed multiple graphs into a multidimensional and possibly non-square hypermesh. This labeling strategy is applicable to the embeddings of other classes of graphs into a hypermesh.