On approximating the minimum independent dominating set
Information Processing Letters
Permutation graphs: connected domination and Steiner trees
Discrete Mathematics - Topics on domination
The complexity of domination problems in circle graphs
Discrete Applied Mathematics
Domination on cocomparability graphs
SIAM Journal on Discrete Mathematics
Steiner set and connected domination in trapezoid graphs
Information Processing Letters
Approximation algorithms for NP-hard problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parameterized domination in circle graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Fast algorithms for min independent dominating set
Discrete Applied Mathematics
Parameterized Domination in Circle Graphs
Theory of Computing Systems
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A graph G = (V, E) is called a circle graph if there is a one-to-one correspondence between vertices in V and a set C of chords in a circle such that two vertices in V are adjacent if and only if the corresponding chords in C intersect. A subset V′ of V is a dominating set of G if for all u ∈ V either u ∈ V′ or u has a neighbor in V′. In addition, if no two vertices in V′ are adjacent, then V′ is called an independent dominating set; if G[V′] is connected, then V′ is called a connected dominating set. Keil (Discrete Applied Mathematics, 42 (1993), 51-63) shows that the minimum dominating set problem and the minimum connected dominating set problem are both NP-complete even for circle graphs. He leaves open the complexity of the minimum independent dominating set problem. In this paper we show that the minimum independent dominating set problem on circle graphs is NP-complete. Furthermore we show that for any Ɛ, 0 ≤ Ɛ nƐ-approximation algorithm for the minimum independent dominating set problem on n-vertex circle graphs, unless P = NP. Several other related domination problems on circle graphs are also shown to be as hard to approximate.