A PTAS for the minimum dominating set problem in unit disk graphs

Authors:
Tim Nieberg;Johann Hurink
Affiliations:
Faculty of Electrical Engineering, Mathematics & Computer Science, University of Twente, Enschede;Faculty of Electrical Engineering, Mathematics & Computer Science, University of Twente, Enschede
Venue:
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Year:
2005

Citing 8
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Abstract

We present a polynomial-time approximation scheme (PTAS) for the minimum dominating set problem in unit disk graphs. In contrast to previously known approximation schemes for the minimum dominating set problem on unit disk graphs, our approach does not assume a geometric representation of the vertices (specifying the positions of the disks in the plane) to be given as part of the input. The runtime of the PTAS is nO(1/εlog 1/ε). The algorithm accepts any undirected graph as input, and returns a (1+ε)-approximate minimum dominating set, or a certificate showing that the input graph is no unit disk graph, making the algorithm robust. The PTAS can easily be adapted to other classes of geometric intersection graphs.