Computing the Girth of a Planar Graph in Linear Time
Data Structures and Algorithms
2015-02-06 v2
Abstract
The girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev, runs in O(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(n log^2 n). Weimann and Yuster further reduced the running time to O(n log n). In this paper, we solve the problem in O(n) time.
Cite
@article{arxiv.1104.4892,
title = {Computing the Girth of a Planar Graph in Linear Time},
author = {Hsien-Chih Chang and Hsueh-I Lu},
journal= {arXiv preprint arXiv:1104.4892},
year = {2015}
}
Comments
20 pages, 7 figures, accepted to SIAM Journal on Computing