A k-partite graph is a graph G = (V1,...,Vk, E), where V1,...,Vk are k non-empty disjoint independent sets of vertices. Such a graph is called complete k-partite if E = Ui ≠ j Vi × Vj. We discuss three variants of the following optimization problem: given a graph and a non-negative weight function on the vertices and edges, find a minimum weight set of vertices and incident edges whose removal from the graph leaves a complete k-partite graph. All the problems we consider are at least as hard to approximate as the weighted vertex cover problem. We use the local-ratio technique to develop 2-approximation algorithms for the first two variants of the problem. In particular, we present the first (linear time) 2-approximation algorithm for the edge clique complement problem. For other previously studied special cases our 2-approximation algorithms are better in terms of time complexity than the existing 2-approximation algorithms. We use approximation preserving reductions in order to (4 - 4/k)-approximate the third variant of the problem.
|Number of pages||21|
|Journal||Journal of Algorithms|
|State||Published - Jan 2002|
Bibliographical noteFunding Information:
1 This research was supported by the Fund for the Promotion of Research at the Technion.
- Approximation algorithm
- Complete k-partite
- Edge deletion
- Local-ratio technique
- Vertex deletion