Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

Abstract. We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollob´as, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k) · n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 23k2 +O(k) · n arithmetic operations and can be efficiently implemented in parallel.

• Type: Conference
• Year: 2009
• Where: ESA
• Authors: Markus Bläser, Christian Hoffmann
• Keywords: Algorithms, ESA 2009, Interlace Polynomial, Multivariate Interlace Polynomial, Tree Decompositions