Fixed-parameter tractability and data reduction for multicut in trees

  • Authors:

  • Jiong Guo;Rolf Niedermeier

  • Affiliations:

  • Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany

  • Venue:
  • Networks
  • Year:
  • 2005

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Abstract

We study an NP-complete (and MaxSNP-hard) communication problem on tree networks, the so-called MULTICUT IN TREES: given an undirected tree and some pairs of nodes of the tree, find out whether there is a set of at most k tree edges whose removal separates all given pairs of nodes. MULTICUT has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomial time approximation algorithms. By way of contrast, we provide a simple fixed-parameter algorithm for MULTICUT IN TREES showing fixed-parameter tractability with respect to parameter k. Moreover, based on some polynomial time data reduction rules, which appear to be of particular interest from an applied point of view, we show a problem kernel for MULTICUT IN TREES by an intricate mathematical analysis. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(3), 124–135 2005