1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor

  • Erik D. Demaine
  • MohammadTaghi Hajiaghayi
  • Dimitrios M. Thilikos
Conference paper

DOI: 10.1007/3-540-45753-4_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2462)
Cite this paper as:
Demaine E.D., Hajiaghayi M., Thilikos D.M. (2002) 1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor. In: Jansen K., Leonardi S., Vazirani V. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2002. Lecture Notes in Computer Science, vol 2462. Springer, Berlin, Heidelberg

Abstract

We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to classes of nonplanar graphs such as K5-minorfree graphs and K3,3-minor-free graphs. Along the way, we present a polynomial-time algorithm to decompose H-minor-free graphs into planar graphs and graphs of treewidth at most cH (a constant dependent on H) using clique sums. This result has several applications in designing fully polynomial-time approximation schemes and fixed-parameter algorithms for many NP-complete problems on these graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • MohammadTaghi Hajiaghayi
    • 1
  • Dimitrios M. Thilikos
    • 2
  1. 1.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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