Efficient computation of the lovász theta function for a class of circulant graphs

Authors:
Valentin E. Brimkov;Reneta P. Barneva;Reinhard Klette;Joseph Straight
Affiliations:
Fairmont State University, Fairmont, West Virginia;State University of New York, Fredonia, NY;CITR Tamaki, University of Auckland, Auckland, New Zealand;State University of New York, Fredonia, NY
Venue:
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2004

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Abstract

We consider the problem of estimating the Shannon capacity of a circulant graph Cn,J of degree four with n vertices and chord length J, 2 ≤ J ≤ n, by computing its Lovász theta function θ(Cn,J). We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation.