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A Pseudo ∈-Approximate Algorithm For Feedback Vertex Set

  • Tianbing Qian
  • Yinyu Ye
  • Panos M. Pardalos
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

While the picture of approximation complexity class becomes clear for most combinatorial optimization problems, it remains an open question whether Feedback Vertex Set can be approximated within a constant ratio in directed graph case. In this paper we present an approximation algorithm with performance bound L max −1, where L max is the largest length of essential cycles in the graph G(V,E). The worst case bound is \(\left\lfloor {\sqrt {{{\left| V \right|}^2} - \left| V \right| - \left| E \right| + 1} } \right\rfloor \) which, in general, is inferior to Seymour’s recent result [14], but becomes a small constant for some graphs. Furthermore, we prove the so-called pseudo ∈-approximate property, i.e. FVS can be divided into a class of disjoint NP -complete subproblems, and our heuristic becomes ∈-approximate for each one of these subproblems.

Keywords

approximation bound feedback vertex set NP -complete 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Tianbing Qian
    • 1
  • Yinyu Ye
    • 1
  • Panos M. Pardalos
    • 2
  1. 1.Department of Management ScienceThe University of IowaIowa CityUSA
  2. 2.Center for Applied Optimization and Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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