On the Minimum Corridor Connection Problem and Other Generalized Geometric Problems

  • Hans Bodlaender
  • Corinne Feremans
  • Alexander Grigoriev
  • Eelko Penninkx
  • René Sitters
  • Thomas Wolle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4368)

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.

Keywords

minimum corridor connection generalized geometric problems complexity exact algorithms approximations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hans Bodlaender
    • 1
  • Corinne Feremans
    • 2
  • Alexander Grigoriev
    • 2
  • Eelko Penninkx
    • 1
  • René Sitters
    • 3
  • Thomas Wolle
    • 4
  1. 1.Institute of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Quantitative EconomicsMaastricht UniversityMaastrichtThe Netherlands
  3. 3.Department of Algorithms and ComplexityMax-Planck-Institute for Computer ScienceSaarbrückenGermany
  4. 4.National ICT Australia LtdAlexandriaAustralia

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