On the minimum corridor connection problem and other generalized geometric problems

  • Authors:

  • Hans Bodlaender;Corinne Feremans;Alexander Grigoriev;Eelko Penninkx;René Sitters;Thomas Wolle

  • Affiliations:

  • Institute of Information and Computing Sciences, Utrecht University, Utrecht, TB, The Netherlands;Department of Quantitative Economics, Maastricht University, Maastricht, MD, The Netherlands;Department of Quantitative Economics, Maastricht University, Maastricht, MD, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, Utrecht, TB, The Netherlands;Department of Algorithms and Complexity, Max-Planck-Institute for Computer Science, Saarbrücken, Germany;National ICT Australia Ltd, Alexandria, NSW, Australia

  • Venue:
  • WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
  • Year:
  • 2006

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Abstract

In this paper we discuss the complexity and approximability of the minimum corridor connection problem where, given a rectilinear decomposition of a rectilinear polygon into “rooms”, one has to find the minimum length tree along the edges of the decomposition such that every room is incident to a vertex of the tree. We show that the problem is strongly NP-hard and give an subexponential time exact algorithm. For the special case of k-outerplanar graphs the running time becomes O(n3). We develop a polynomial time approximation scheme for the case when all rooms are fat and have nearly the same size. When rooms are fat but are of varying size we give a polynomial time constant factor approximation algorithm.