A PTAS for the Minimum Dominating Set Problem in Unit Disk Graphs
نویسندگان
چکیده
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 algorithm accepts any undirected graph as input, and is robust in the sense that for instances not reflecting unit disk graphs, it either returns a (1+ ε)-approximate minimum dominating set, or a certificate showing that the input graph is no unit disk graph. The given PTAS can easily be adapted to other classes of related geometric intersection graphs.
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