Into the square: On the complexity of some quadratic-time solvable problems

M Borassi, P Crescenzi, M Habib - Electronic Notes in Theoretical …, 2016 - Elsevier
We analyze several quadratic-time solvable problems, and we show that these problems are
not solvable in truly subquadratic time (that is, in time O (n 2− ϵ) for some ϵ> 0), unless the …

Computationally tractable riemannian manifolds for graph embeddings

C Cruceru, G Bécigneul, OE Ganea - Proceedings of the AAAI …, 2021 - ojs.aaai.org
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds
has recently gained momentum in machine learning due to their desirable geometric …

Fully polynomial FPT algorithms for some classes of bounded clique-width graphs

D Coudert, G Ducoffe, A Popa - ACM Transactions on Algorithms (TALG), 2019 - dl.acm.org
Recently, hardness results for problems in P were achieved using reasonable complexity-
theoretic assumptions such as the Strong Exponential Time Hypothesis. According to these …

On computing the hyperbolicity of real-world graphs

M Borassi, D Coudert, P Crescenzi… - Algorithms-ESA 2015: 23rd …, 2015 - Springer
The (Gromov) hyperbolicity is a topological property of a graph, which has been recently
applied in several different contexts, such as the design of routing schemes, network …

[HTML][HTML] Applying clique-decomposition for computing Gromov hyperbolicity

N Cohen, D Coudert, G Ducoffe, A Lancin - Theoretical computer science, 2017 - Elsevier
Given a graph, its hyperbolicity is a measure of how close its distance distribution is to the
one of a tree. This parameter has gained recent attention in the analysis of some graph …

Fast approximation and exact computation of negative curvature parameters of graphs

J Chalopin, V Chepoi, FF Dragan, G Ducoffe… - Discrete & …, 2021 - Springer
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 …

When can graph hyperbolicity be computed in linear time?

T Fluschnik, C Komusiewicz, GB Mertzios, A Nichterlein… - Algorithmica, 2019 - Springer
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 …

[HTML][HTML] On the hyperbolicity of bipartite graphs and intersection graphs

D Coudert, G Ducoffe - Discrete Applied Mathematics, 2016 - Elsevier
Hyperbolicity is a measure of the tree-likeness of a graph from a metric perspective.
Recently, it has been used to classify complex networks depending on their underlying …

Discrete-time gradient flows in Gromov hyperbolic spaces

S Ohta - arXiv preprint arXiv:2205.03156, 2022 - arxiv.org
We investigate fundamental properties of the proximal point algorithm for Lipschitz convex
functions on (proper, geodesic) Gromov hyperbolic spaces. We show that the proximal point …

[HTML][HTML] Data center interconnection networks are not hyperbolic

D Coudert, G Ducoffe - Theoretical Computer Science, 2016 - Elsevier
Topologies for data center interconnection networks have been proposed in the literature
through various graph classes and operations. A common trait to most existing designs is …