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.

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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