Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Computer Science

Profile

Publication details for Dr George Mertzios

Fluschnik, T., Komusiewicz, C., Mertzios, G.B., Nichterlein, A., Niedermeier, R. & Talmon, N. (2019). When can graph hyperbolicity be computed in linear time? Algorithmica 81(5): 2016–2045.

Author(s) from Durham

Abstract

Hyperbolicity is a distance-based measure of how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known algorithms used in practice for computing the hyperbolicity number of an n-vertex graph have running time O(n4) . Exploiting the framework of parameterized complexity analysis, we explore possibilities for “linear-time FPT” algorithms to compute hyperbolicity. For example, we show that hyperbolicity can be computed in 2O(k)+O(n+m) time (where m and k denote the number of edges and the size of a vertex cover in the input graph, respectively) while at the same time, unless the Strong Exponential Time Hypothesis (SETH) fails, there is no 2o(k)⋅n2−ε -time algorithm for every ε>0 .