Chakraborty, D. orcid.org/0000-0003-0534-6417 and Vaxès, Y. (Accepted: 2025) Additive approximation algorithm for geodesic centers in δ-hyperbolic graphs. Theoretical Computer Science. ISSN 0304-3975 (In Press)
Abstract
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 & Zaks (Networks, 1994) 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 & Leitert, (TCS, 2017) to show that for every k ≥ 1, k-Geodesic Center is NP-hard even on partial grids.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in Theoretical Computer Science, made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Hyperbolicity, approximation algorithms, Isometric paths, Minimum eccentricity shortest paths |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 29 May 2025 09:40 |
Last Modified: | 30 May 2025 13:36 |
Status: | In Press |
Publisher: | Elsevier |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:227151 |