Paper by Erik D. Demaine

Reference:

Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dimitrios M. Thilikos, “1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor”, in Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2002), Lecture Notes in Computer Science, volume 2462, Rome, Italy, September 17–21, 2002, pages 67–80.

BibTeX

@InProceedings{CliqueSum_APPROX2002,
  AUTHOR        = {Erik D. Demaine and MohammadTaghi Hajiaghayi and
                   Dimitrios M. Thilikos},
  TITLE         = {1.5-Approximation for Treewidth of Graphs Excluding a Graph
                   with One Crossing as a Minor},
  BOOKTITLE     = {Proceedings of the 5th International Workshop on
                   Approximation Algorithms for Combinatorial Optimization
                   Problems (APPROX 2002)},
  bookurl       = {http://www.dis.uniroma1.it/~algo02/approx02/},
  SERIES        = {Lecture Notes in Computer Science},
  SERIESURL     = {http://www.springer.de/comp/lncs/},
  VOLUME        = 2462,
  ADDRESS       = {Rome, Italy},
  MONTH         = {September 17--21},
  YEAR          = 2002,
  PAGES         = {67--80},

  copyright     = {The paper is \copyright Springer-Verlag.},
  length        = {14 pages},
  papers        = {CliqueSum_JCSS; CliqueSum_ISAAC2002},
  withstudent   = 1,
  doi           = {https://dx.doi.org/10.1007/3-540-45753-4_8},
  dblp          = {https://dblp.org/rec/conf/approx/DemaineHT02},
}

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-minor-free 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.

Copyright:

The paper is \copyright Springer-Verlag.

Length:

The paper is 14 pages.

Availability:

The paper is available in PostScript (213k) and PDF (169k).

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Related papers:

CliqueSum_JCSS (Approximation algorithms for classes of graphs excluding single-crossing graphs as minors)

CliqueSum_ISAAC2002 (Exponential Speedup of Fixed-Parameter Algorithms on K_3,3-minor-free or K₅-minor-free Graphs)