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Primal-dual approximation algorithms for feedback problems in planar graphs

  • Michel X. Goemans
  • David P. Williamson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1084)

Abstract

Given a subset of cycles of a graph, we consider the problem of finding a minimum-weight set of vertices that meets all cycles in the subset. This problem generalizes a number of problems, including the minimum-weight feedback vertex set problem in both directed and undirected graphs, the subset feedback vertex set problem, and the graph bipartization problem, in which one must remove a minimum-weight set of vertices so that the remaining graph is bipartite. We give a 9/4-approximation algorithm for the general problem in planar graphs, given that the subset of cycles obeys certain properties. This results in 9/4-approximation algorithms for the aforementioned feedback and bipartization problems in planar graphs. Our algorithms use the primaldual method for approximation algorithms as given in Goemans and Williamson [14]. We also show that our results have an interesting bearing on a conjecture of Akiyama and Watanabe [2] on the cardinality of feedback vertex sets in planar graphs.

Keywords

Approximation Algorithm Planar Graph Undirected Graph Network Design Problem Linear Programming Relaxation 
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

  • Michel X. Goemans
    • 1
  • David P. Williamson
    • 2
  1. 1.Dept. of MathematicsM.I.T.Cambridge
  2. 2.IBM T.J. Watson Research CenterYorktown Heights

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