Approximating element-weighted vertex deletion problems for the complete k-partite property

Reuven Bar-Yehuda, Dror Rawitz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Pages (from-to)20-40
Number of pages21
JournalJournal of Algorithms
Issue number1
StatePublished - Jan 2002
Externally publishedYes

Bibliographical note

Funding 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


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