A (2+epsilon)-approximation scheme for minimum domination on circle graphs

Abstract

The main result of this paper is a (2 + epsilon)-approximation scheme for the minimum dominating set problem on circle graphs. We first present an O(n(2)) time 8-approximation algorithm for this problem and then extend it to an O(n(3) + 6/epsilonn([6/epsilon+1])m) time (2 + epsilon)-approximation scheme for this problem. Here n and m are the number of vertices and the number of edges of the circle graph. We then present simple modifications to this algorithm that yield (3 + epsilon)-approximation schemes for the minimum connected and the minimum total dominating set problems on circle graphs. Keil (1993, Discrete Appl. Math. 42, 51-63) shows that these problems are NP-complete for circle graphs and leaves open the problem of devising approximation algorithms for them. These are the first O(1)-approximation algorithms for domination problems on circle graphs. .