TY - GEN

T1 - When can graph hyperbolicity be computed in linear time?

AU - Fluschnik, Till

AU - Komusiewicz, Christian

AU - Mertzios, George B.

AU - Nichterlein, André

AU - Niedermeier, Rolf

AU - Talmon, Nimrod

N1 - Funding Information:
C. Komusiewicz — Supported by the DFG, project MAGZ (KO 3669/4-1).
Funding Information:
A. Nichterlein — Supported by a postdoctoral fellowship of the DAAD while at Durham University.
Funding Information:
T. Fluschnik — Supported by the DFG, project DAMM (NI 369/13-2).
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Hyperbolicity measures, in terms of (distance) metrics, 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 practical algorithms for computing the hyperbolicity number of a 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 instance, we show that hyperbolicity can be computed in time 2O(k) + O(n + m) (m being the number of graph edges, k being the size of a vertex cover) while at the same time, unless the SETH fails, there is no 2o(k)n2-time algorithm.

AB - Hyperbolicity measures, in terms of (distance) metrics, 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 practical algorithms for computing the hyperbolicity number of a 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 instance, we show that hyperbolicity can be computed in time 2O(k) + O(n + m) (m being the number of graph edges, k being the size of a vertex cover) while at the same time, unless the SETH fails, there is no 2o(k)n2-time algorithm.

UR - http://www.scopus.com/inward/record.url?scp=85025145105&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-62127-2_34

DO - 10.1007/978-3-319-62127-2_34

M3 - Conference contribution

AN - SCOPUS:85025145105

SN - 9783319621265

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 397

EP - 408

BT - Algorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings

A2 - Ellen, Faith

A2 - Kolokolova, Antonina

A2 - Sack, Jorg-Rudiger

PB - Springer Verlag

T2 - 15th International Symposium on Algorithms and Data Structures, WADS 2017

Y2 - 31 July 2017 through 2 August 2017

ER -