ï¿½ Springer-Verlag GmbH Germany 2016. A vertex set X of a graph G is an association set if each component of G − X is a clique, or a dissociation set if each component of G − X is a single vertex or a single edge. Interestingly, G − X is then precisely a graph containing no induced P3’s or containing no P3’s, respectively. We observe some special structures and show that if none of them exists, then the minimum association set problem can be reduced to the minimum (weighted) dissociation set problem. This yields the first nontrivial approximation algorithm for the association set problem, with approximation ratio is 2.5. The reduction is based on a combinatorial study of modular decomposition of graphs free of these special structures. Further, a novel algorithmic use of modular decomposition enables us to implement this approach in O(mn + n2) time.
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||42nd International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2016|
|Period||22/06/16 → 24/06/16|
- Theoretical Computer Science
- Computer Science(all)