Line-distortion, Bandwidth and Path-length of a graph
Abstract
We investigate the minimum line-distortion and the minimum bandwidth problems on unweighted graphs and their relations with the minimum length of a Robertson-Seymour's path-decomposition. The length of a path-decomposition of a graph is the largest diameter of a bag in the decomposition. The path-length of a graph is the minimum length over all its path-decompositions. In particular, we show: - if a graph can be embedded into the line with distortion , then admits a Robertson-Seymour's path-decomposition with bags of diameter at most in ; - for every class of graphs with path-length bounded by a constant, there exist an efficient constant-factor approximation algorithm for the minimum line-distortion problem and an efficient constant-factor approximation algorithm for the minimum bandwidth problem; - there is an efficient 2-approximation algorithm for computing the path-length of an arbitrary graph; - AT-free graphs and some intersection families of graphs have path-length at most 2; - for AT-free graphs, there exist a linear time 8-approximation algorithm for the minimum line-distortion problem and a linear time 4-approximation algorithm for the minimum bandwidth problem.
Cite
@article{arxiv.1409.8389,
title = {Line-distortion, Bandwidth and Path-length of a graph},
author = {Feodor F. Dragan and Ekkehard Köhler and Arne Leitert},
journal= {arXiv preprint arXiv:1409.8389},
year = {2014}
}