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. We provide the bounds for 5 ≤ d ≤ 12. The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to find bisections of d-regular graphs. We also give empirical values of the size of bisection found by the algorithm for some small values of d and compare it with numerical approximations of our theoretical bounds. Our analysis also gives asymptotic lower bounds for the size of the maximum bisection.
The work of the first and second authors was partially supported by the IST programme of the EU under contract IST-1999-14186 (ALCOM-FT). The first author is also supported by the Distinció per a la recerca of the Generalitat de Catalunya. The second author is also supported by the Spanish CICYT project TIC-2002-04498-C05-03. The third author is supported by the Canada Research Chairs Program and partially by the Australian Research Council when this author was at the University of Melbourne.
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Díaz, J., Serna, M.J., Wormald, N.C. (2004). Computation of the Bisection Width for Random d-Regular Graphs. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_9
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DOI: https://doi.org/10.1007/978-3-540-24698-5_9
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