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

https://doi.org/10.1016/j.tcs.2010.07.017Get rights and content
Under an Elsevier user license
open archive

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 g×g grid as a minor. Let c1 be a fixed integer and α,β arbitrary constants satisfying α>c+1 and β>2c+1. We give an algorithm which constructs in O(n1+1clogn) time a branch-decomposition of G with width at most αbw(G). We also give an algorithm which constructs a g×g grid minor of G with ggm(G)β in O(n1+1clogn) time. The constants hidden in the Big-O notations are proportional to cα(c+1) and cβ(2c+1), respectively.

Keywords

Graph algorithms
Branch-decompositions
Graph minors

Cited by (0)

A preliminary version of this paper appeared in (Q.P. Gu, H. Tamaki, Constant-factor approximations of branch-decomposition and largest grid minor of planar graphs in O(n1+ϵ) time, in: Proc. of the 2009 International Symposium on Algorithms and Computation, ISAAC 2009, 2009, pp. 984–993) [19].