ALCOMFT-TR-03-65

Fedor V. Fomin and Dimitrios M. Thilikos
New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
Barcelona. Work packages 2 and 4. October 2003.

Abstract: It is known that a planar graph on n vertices has branch-width/tree-width bounded by alpha\sqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-width, alpha<3.182 and for the case of branch-width, alpha<2.122. Our proof is based on the planar separation theorem of Alon, Seymour & Thomas and some min-max theorems of Robertson & Seymour from the graph minors series.

Based on these bounds we introduce a new method for solving different fixed parameter problems on planar graphs. We prove that our method provides the best so far exponential speed-up for fundamental problems on planar graphs like \textscVertex Cover, \textscDominating Set and many others.

Postscript file: ALCOMFT-TR-03-65.ps.gz (404 kb).