Polynomial-time data reduction for dominating set

Authors:
Jochen Alber;Michael R. Fellows;Rolf Niedermeier
Affiliations:
Universität Tübingen, Tübingen, Germany;University of Newcastle, Callaghan, Australia;Universität Tübingen, Tübingen, Germany
Venue:
Journal of the ACM (JACM)
Year:
2004

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Abstract

Dealing with the NP-complete Dominating Set problem on graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy-to-implement reduction rules. Moreover, having implemented our reduction rules, first experiments indicate the impressive practical potential of these rules. Thus, this work seems to open up a new and prospective way how to cope with one of the most important problems in graph theory and combinatorial optimization.