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New graph decompositions with applications to emulations

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Abstract

In this paper we present a new type of graph decomposition calleda cut-cover that combines the notions of graph separators andt-neighborhood covers. We show that graphs with good cut-covers can be emulated in hypercubes and we show that planar and certain minor-excluded graphs have good cut-covers.

In particular, we show how to emulate anyN-node bounded degree planar graph or anyN-node bounded degree graph that excludes \(K_{log^{0(1)} N} \) as a minor with constant slowdown on hypercube networks.

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The research of C. Kaklamanis and D. Krizanc was supported in part by the NEC Research Institute.

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Kaklamanis, C., Krizanc, D. & Rao, S. New graph decompositions with applications to emulations. Theory of Computing Systems 30, 39–49 (1997). https://doi.org/10.1007/BF02679452

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