@article{7691ab8478264e168d1fd5229a79526e,

title = "When Can Graph Hyperbolicity be Computed in Linear Time?",

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 2 O(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 2 o(k)· n2-ε-time algorithm for every ε> 0.",

keywords = "Cographs, FPT in P, Parameterized complexity, Polynomial-time algorithm, Strong Exponential Time Hypothesis, Vertex cover number",

author = "Till Fluschnik and Christian Komusiewicz and Mertzios, {George B.} and Andr{\'e} Nichterlein and Rolf Niedermeier and Nimrod Talmon",

note = "Funding Information: We are grateful to the anonymous reviewers of WADS{\textquoteright}17 and Algorithmica for their comments. TF acknowledges support by the DFG, Projects DAMM (NI 369/13-2) and TORE (NI 369/18). CK acknowledges support by the DFG, Project MAGZ (KO 3669/4-1). GM acknowledges support by the EPSRC Grant EP/P020372/1. AN acknowledges support by a postdoctoral fellowship of the DAAD while at Durham University. NT acknowledges support by a postdoctoral fellowship from I-CORE ALGO. Funding Information: Acknowledgements We are grateful to the anonymous reviewers of WADS{\textquoteright}17 and Algorithmica for their comments. TF acknowledges support by the DFG, Projects DAMM (NI 369/13-2) and TORE (NI 369/18). CK acknowledges support by the DFG, Project MAGZ (KO 3669/4-1). GM acknowledges support by the EPSRC Grant EP/P020372/1. AN acknowledges support by a postdoctoral fellowship of the DAAD while at Durham University. NT acknowledges support by a postdoctoral fellowship from I-CORE ALGO. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

month = may,

day = "15",

doi = "10.1007/s00453-018-0522-6",

language = "English",

volume = "81",

pages = "2016--2045",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "5",

}