Embedding of hypercubes into grids
We consider one-to-one embeddings of the n-dimensional hypercube into grids with 2n vertices and present lower and upper bounds and asymptotic estimates for minimal dilation, edge-congestion, and their mean values. We also introduce and study two new cost-measures for these embeddings, namely the sum over i=1, ..., n of dilations and the sum of edge-congestions caused by the hypercube edges of the ith dimension. It is shown that, in the simulation via the embedding approach, such measures are much more suitable for evaluating the slowdown of uniaxial hypercube algorithms then the traditional cost measures.
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- 2.Bezrukov, S.L., Chavez, J.D., Harper, L.H., Röttger M., Schroeder U.-P.: The congestion of n-cube layout on a rectangular grid, to appear in Disc. Mathematics.Google Scholar
- 3.Bezrukov, S.L., Röttger, M., Schroeder, U.-P.: Embedding of hypercubes into grids. Technical Report tr-sfb-95-1, University of Paderborn, (1995).Google Scholar
- 7.Katona, G.O.H.: A theorem on finite sets. In: Theory of Graphs, Akademia Kiado, Budapest, (1968), 187–207.Google Scholar
- 9.Nakano, K.: Linear layout of generalized hypercubes. In: Proc. Graph-Theoretic Concepts in Computer Science, LNCS 790, Springer Verlag, (1994), 364–375.Google Scholar
- 10.Zienicke, P.: Embedding hypercubes in 2-dimensional meshes. Humboldt-Universität zu Berlin, (manuscript).Google Scholar