Experimental evaluation of a tree decomposition-based algorithm for vertex cover on planar graphs

  • Authors:

  • Jochen Alber;Frederic Dorn;Rolf Niedermeier

  • Affiliations:

  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Fed. Rep. of Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Fed. Rep. of Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Fed. Rep. of Germany

  • Venue:
  • Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
  • Year:
  • 2005

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Abstract

Many NP-complete problems on planar graphs are "fixed-parameter tractable:" Recent theoretical work provided tree decomposition-based fixed-parameter algorithms exactly solving various parameterized problems on planar graphs, among others VERTEX COVER, in time O(c√kn). Here, c is some constant depending on the graph problem to be solved, n is the number of graph vertices, and k is the problem parameter (for VERTEX COVER this is the size of the vertex cover).In this paper, we present an experimental study for such tree decomposition-based algorithms focusing on VERTEX COVER. We demonstrate that the tree decomposition-based approach provides a valuable way of exactly solving VERTEX COVER on planar graphs. Doing so, we also demonstrate the impressive power of the so-called Nemhauser/Trotter theorem which provides a VERTEX COVER-specific, extremely useful data reduction through polynomial time preprocessing. Altogether, this underpins the practical importance of the underlying theory.