Treewidth Lower Bounds with Brambles

Authors:
Hans L. Bodlaender;Alexander Grigoriev;Arie M. C. A. Koster
Affiliations:
Utrecht University, Department of Information and Computing Sciences, P.O. Box 80.089, 3508, Utrecht, TB, The Netherlands;University of Maastricht, Department of Quantitative Economics, P.O. Box 616, 6200, Maastricht, MD, The Netherlands;Zuse Institute Berlin (ZIB), P.O. Box 616, Takustraße 7, 14195, Berlin-Dahlem, MD, Germany
Venue:
Algorithmica
Year:
2008

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Abstract

In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph G is the maximum order of a bramble of G minus one. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a lower bound for both the treewidth and branchwidth that is at most a constant factor away from the optimum. For both algorithms, we report on extensive computational experiments that show that the algorithms often give excellent lower bounds, in particular when applied to (close to) planar graphs.