Additive approximation algorithm for geodesic centers in δ-hyperbolic graphs

For an integer k≥1, the objective of k-Geodesic Center is to find a set C of k isometric paths such that the maximum distance between any vertex v and C is minimised. Introduced by Gromov, δ-hyperbolicity measures how treelike a graph is from a metric point of view. Our main contribution in this pap...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1049; p. 115365
Main Authors: Chakraborty, Dibyayan, Vaxès, Yann
Format: Journal Article
Language:English
Published: Elsevier B.V 17.09.2025
Subjects:
Approximation algorithms
Hyperbolicity
Isometric paths
Minimum eccentricity shortest paths
Approximation algorithms
Hyperbolicity
Isometric paths
Minimum eccentricity shortest paths
ISSN:0304-3975
Online Access:Get full text
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Summary:For an integer k≥1, the objective of k-Geodesic Center is to find a set C of k isometric paths such that the maximum distance between any vertex v and C is minimised. Introduced by Gromov, δ-hyperbolicity measures how treelike a graph is from a metric point of view. Our main contribution in this paper is to provide an additive O(δ)-approximation algorithm for k-Geodesic Center on δ-hyperbolic graphs. On the way, we define a coarse version of the pairing property introduced by Gerstel and Zaks (1994) [28] and show it holds for δ-hyperbolic graphs. This result allows to reduce the k-Geodesic Center problem to its rooted counterpart, a main idea behind our algorithm. We also adapt a technique of Dragan and Leitert (2017) [24] to show that for every k≥1, k-Geodesic Center is NP-hard even on partial grids.
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115365