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A unified local ratio approximation of node-deletion problems

Extended abstract
  • Toshihiro Fujito
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)

Abstract

In this paper we consider a unified approximation method for node-deletion problems with nontrivial and hereditary graph properties. It was proved 16 years ago that every node-deletion problems for a nontrivial hereditary property is NP-complete via a few generic approximation preserving reductions from the Vertex Cover problem. An open problem posed at that time is concerned with the other direction of approximability: can other node-deletion problems be approximated as good as the Vertex Cover ?

The goal of the current paper is to take a first step along the direction of research suggested above. More specifically, one generic approximation algorithm is presented, which is applicable to every node-deletion problem for a hereditary property. It will be seen then that under simple and natural weighting schemes, serving as a parameter of the algorithm, various node-deletion problems can be approximated with ratio 2, or otherwise with some nontrivial performance ratios. Two types of graph properties are considered in this paper: one with a finite number of minimal forbidden graphs, and the other in which all the edge sets of satisfying (sub)graphs form a family of independent sets for some matroid.

Keywords

Node Degree Performance Ratio Minimal Solution Graph Property Hereditary Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Toshihiro Fujito
    • 1
  1. 1.Dept. of Electrical Engineering, Faculty of EngineeringHiroshima UniversityHigashi-HiroshimaJapan

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