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ESA
2009
Springer

Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

9 years 2 months ago
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.
Markus Bläser, Christian Hoffmann
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where ESA
Authors Markus Bläser, Christian Hoffmann
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