A Quadratic Vertex Kernel for Feedback Arc Set in Bipartite Tournaments

  • Mingyu Xiao
  • Jiong Guo
Conference paper

DOI: 10.1007/978-3-642-32589-2_71

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)
Cite this paper as:
Xiao M., Guo J. (2012) A Quadratic Vertex Kernel for Feedback Arc Set in Bipartite Tournaments. In: Rovan B., Sassone V., Widmayer P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg

Abstract

The k-feedback arc set problem is to determine whether there is a set F of at most k arcs in a directed graph G such that the removal of F makes G acyclic. The k-feedback arc set problems in tournaments and bipartite tournaments (k-FAST and k-FASBT) have applications in ranking aggregation and have been extensively studied from the viewpoint of parameterized complexity. Recently, Misra et al. provide a problem kernel with O(k3) vertices for k-FASBT. Answering an open question by Misra et al., we improve the kernel bound to O(k2) vertices by introducing a new concept called “bimodule.”

Keywords

Kernelization Feedback arc set Bipartite tournament Graph algorithms Parameterized algorithms 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mingyu Xiao
    • 1
  • Jiong Guo
    • 2
  1. 1.School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Universität des SaarlandesSaarbrückenGermany

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