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

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(C n,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. © Springer-Verlag 2004.