Approximation hardness of dominating set problems in bounded degree graphs

Authors:
M. Chlebík;J. Chlebíková
Affiliations:
Department of Mathematics, University of Sussex, Brighton BN1 9RF, UK;Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
Venue:
Information and Computation
Year:
2008

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Abstract

We study approximation hardness of the Minimum Dominating Set problem and its variants in undirected and directed graphs. Using a similar result obtained by Trevisan for Minimum Set Cover we prove the first explicit approximation lower bounds for various kinds of domination problems (connected, total, independent) in bounded degree graphs. Asymptotically, for degree bound approaching infinity, these bounds almost match the known upper bounds. The results are applied to improve the lower bounds for other related problems such as Maximum Induced Matching and Maximum Leaf Spanning Tree.