APX-hardness of domination problems in circle graphs

Authors:
Mirela Damian;Sriram V. Pemmaraju
Affiliations:
Department of Computer Science, Villanova University, Villanova, PA 19085, USA;Department of Computer Science, University of Iowa, Iowa City, IA 52242, USA
Venue:
Information Processing Letters
Year:
2006

Citing 7
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Abstract

We show that the problem of finding a minimum dominating set in a circle graph is APX-hard: there is a constant @d0 such that there is no (1+@d)-approximation algorithm for the minimum dominating set problem on circle graphs unless P=NP. Hence a PTAS for this problem seems unlikely. This hardness result complements the (2+@?)-approximation algorithm for the problem [M. Damian, S.V. Pemmaraju, A (2+@?)-approximation scheme for minimum domination on circle graphs, J. Algorithms 42 (2) (2002) 255-276].