## 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(n^{4}). 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}^{)}· n^{2}^{-}^{ε}-time algorithm for every ε> 0.

Original language | English |
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Pages (from-to) | 2016-2045 |

Number of pages | 30 |

Journal | Algorithmica |

Volume | 81 |

Issue number | 5 |

DOIs | |

State | Published - 15 May 2019 |

## Keywords

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

## ASJC Scopus subject areas

- General Computer Science
- Computer Science Applications
- Applied Mathematics