Constant-factor approximations of branch-decomposition and largest grid minor of planar graphs in O(n1+) time

  • Authors:

  • Qian-Ping Gu;Hisao Tamaki

  • Affiliations:

  • School of Computing Science, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada;Department of Computer Science, Meiji University, 1-1-1 Higashi-mita, Tamaku, Kawasaki-shi, 214-8571, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2011

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Abstract

We give constant-factor approximation algorithms for computing the optimal branch-decompositions and largest grid minors of planar graphs. For a planar graph G with n vertices, let bw(G) be the branchwidth of G and gm(G) the largest integer g such that G has a gxg grid as a minor. Let c=1 be a fixed integer and @a,@b arbitrary constants satisfying @ac+1 and @b2c+1. We give an algorithm which constructs in O(n^1^+^1^clogn) time a branch-decomposition of G with width at most @abw(G). We also give an algorithm which constructs a gxg grid minor of G with g=gm(G)@b in O(n^1^+^1^clogn) time. The constants hidden in the Big-O notations are proportional to c@a-(c+1) and c@b-(2c+1), respectively.