Bandwidth and Distortion Revisited

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) time and polynomial space. For BANDWIDTH, this improves O(10) algorithm by Feige and Kilian from 2000, for DISTORTION this is the first polynomial space exact algorithm that works in O(c) time we are aware of. As a coproduct, we enhance the O(5)–time and O(2)–space algorithm for DISTORTION by Fomin et al. to an algorithm working in O(4.383) time and space.