Counting minimum weighted dominating sets

Authors:
Fedor V. Fomin;Alexey A. Stepanov
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Year:
2007

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Abstract

We show how to count all minimum weighted dominating sets of a graph on n vertices in time O(1.5535n). Our algorithm is a combination of branch and bound approach along with dynamic programming on graphs with bounded treewidth. To achieve O(1.5535n) bound we introduce a technique of measuring running time of our algorithm by combining measure and conquer approach with linear programming.