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International Workshop on Approximation Algorithms for Combinatorial Optimization

APPROX 2002: Approximation Algorithms for Combinatorial Optimization pp 67–80Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2462))

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 K 5-minorfree graphs and K 3,3-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 c H (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.

The work of the third author was supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT), the Spanish CICYT project TIC2000-1970-CE, and the Ministry of Education and Culture of Spain (Resolución 31/7/00 - BOE 16/8/00).

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Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, 200 Technology Square, 02139, Cambridge, MA, USA

    Erik D. Demaine & MohammadTaghi Hajiaghayi

  2. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord - Mòdul C5, Desp. 211b, c/Jordi Girona Salgado, 1-3, E-08034, Barcelona, Spain

    Dimitrios M. Thilikos

Authors
  1. Erik D. Demaine
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  2. MohammadTaghi Hajiaghayi
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  3. Dimitrios M. Thilikos
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Editor information

Editors and Affiliations

  1. Institut für Informatik und praktische Mathematik, Universität Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  2. Dipartimento di Informatika e Sistemistica, Universita di Roma La Sapienza, Via Salaria 113, 00198, Roma, Italy

    Stefano Leonardi

  3. College of Computing, Georgia Institute of Technology, 801 Atlantic Drive, Atlanta, 30332-0280, Georgia, USA

    Vijay Vazirani

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© 2002 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/3-540-45753-4_8

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  • DOI: https://doi.org/10.1007/3-540-45753-4_8

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