Recognizing circle graphs in polynomial time
Journal of the ACM (JACM)
The complexity of domination problems in circle graphs
Discrete Applied Mathematics
Journal of Algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Approximation algorithms
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
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We show that the problem of finding a minimum dominating set in a circle graph is APX-hard: there is a constant δ 0 such that there is no (1 + δ)-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 + ε)-approximation algorithm for the problem [M. Damian, S.V. Pemmaraju, A (2 + ε)-approximation scheme for minimum domination on circle graphs, J. Algorithms 42 (2) (2002) 255-276].