Polynomial Time Data Reduction for Dominating Set

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.

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Jochen Alber, Michael R. Fellows, Rolf Niedermeier
• Keywords: CORR 2002, Dominating Set, Dominating Set Problem, Education, Reduction Rules