Bandwidth and Distortion Revisited
Data Structures and Algorithms
2010-04-29 v1
Abstract
In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes distortion (the DISTORTION problem). For both problems we develop algorithms that work in O(9.363^n) time and polynomial space. For BANDWIDTH, this improves O^*(10^n) algorithm by Feige and Kilian from 2000, for DISTORTION this is the first polynomial space exact algorithm that works in O(c^n) time we are aware of. As a byproduct, we enhance the O(5^{n+o(n)})-time and O^*(2^n)-space algorithm for DISTORTION by Fomin et al. to an algorithm working in O(4.383^n) time and space.
Cite
@article{arxiv.1004.5012,
title = {Bandwidth and Distortion Revisited},
author = {Marek Cygan and Marcin Pilipczuk},
journal= {arXiv preprint arXiv:1004.5012},
year = {2010}
}