When Can Graph Hyperbolicity Be Computed in Linear Time?
نویسندگان
چکیده
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(n). 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 2 + 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 2n-time algorithm.
منابع مشابه
Hyper
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 algorithms for computing the hyperbolicity number of a graph (the smaller, the more tree-like) have running time O(n), where n is the number of graph ...
متن کاملTenacity and some other Parameters of Interval Graphs can be computed in polynomial time
In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...
متن کاملFast approximation and exact computation of negative curvature parameters of graphs
In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to the study of graph hyperbolicity. Our main contribution in this note is a new characterization of hyperbolicity for graphs (and for complete geodesic metric ...
متن کاملCop and robber game and hyperbolicity
In this note, we prove that all cop-win graphs G in the game in which the robber and the cop move at different speeds s and s′ with s′ < s, are δ-hyperbolic with δ = O(s). We also show that the dependency between δ and s is linear if s − s′ = Ω(s) and G obeys a slightly stronger condition. This solves an open question from the paper J. Chalopin et al., Cop and robber games when the robber can h...
متن کاملON THE SZEGED INDEX OF NON-COMMUTATIVE GRAPH OF GENERAL LINEAR GROUP
Let $G$ be a non-abelian group and let $Z(G)$ be the center of $G$. Associate with $G$ there is agraph $Gamma_G$ as follows: Take $Gsetminus Z(G)$ as vertices of$Gamma_G$ and joint two distinct vertices $x$ and $y$ whenever$yxneq yx$. $Gamma_G$ is called the non-commuting graph of $G$. In recent years many interesting works have been done in non-commutative graph of groups. Computing the clique...
متن کامل