Bounds on the bisection width for random d -regular graphs

Authors:
J. Díaz;M. J. Serna;N. C. Wormald
Affiliations:
Dept. Llenguatges i Sistemes, Universitat Politecnica de Catalunya, Jordi Girona Salgado 13, 08034 Barcelona, Spain;Dept. Llenguatges i Sistemes, Universitat Politecnica de Catalunya, Jordi Girona Salgado 13, 08034 Barcelona, Spain;Dept. Combinatorics and Optimization, University of Waterloo, Canada N2L 3G1
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

In this paper we provide an explicit way to compute asymptotically almost sure upper bounds on the bisection width of random d-regular graphs, for any value of d. The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to find bisections of d-regular graphs. We provide bounds for 5≤d≤12. We also give empirical values of the size of the bisection found by the algorithm for some small values of d and compare them with numerical approximations of our theoretical bounds. Our analysis also gives asymptotic lower bounds for the size of the maximum bisection.