Theory of Computing Systems

, Volume 53, Issue 4, pp 609–620 | Cite as

A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments

  • Pranabendu Misra
  • Venkatesh Raman
  • M. S. Ramanujan
  • Saket Saurabh
Article

Abstract

In the k-Feedback Arc/Vertex Set problem we are given a directed graph D and a positive integer k and the objective is to check whether it is possible to delete at most k arcs/vertices from D to make it acyclic. Dom et al. (J. Discrete Algorithm 8(1):76–86, 2010) initiated a study of the Feedback Arc Set problem on bipartite tournaments (k-FASBT) in the realm of parameterized complexity. They showed that k-FASBT can be solved in time O(3.373kn6) on bipartite tournaments having n vertices. However, until now there was no known polynomial sized problem kernel for k-FASBT. In this paper we obtain a cubic vertex kernel for k-FASBT. This completes the kernelization picture for the Feedback Arc/Vertex Set problem on tournaments and bipartite tournaments, as for all other problems polynomial kernels were known before. We obtain our kernel using a non-trivial application of “independent modules” which could be of independent interest.

Keywords

Kernelization Feedback arc set Bipartite tournament 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Pranabendu Misra
    • 1
  • Venkatesh Raman
    • 1
  • M. S. Ramanujan
    • 1
  • Saket Saurabh
    • 1
  1. 1.Institute of Mathematical SciencesTaramaniIndia

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