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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| Published in: | Theoretical computer science Vol. 1049; p. 115365 |
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| 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 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. |
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| AbstractList | 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. |
| ArticleNumber | 115365 |
| Author | Chakraborty, Dibyayan Vaxès, Yann |
| Author_xml | – sequence: 1 givenname: Dibyayan orcidid: 0000-0003-0534-6417 surname: Chakraborty fullname: Chakraborty, Dibyayan email: D.chakraborty@leeds.ac.uk organization: School of Computer Science, University of Leeds, United Kingdom – sequence: 2 givenname: Yann surname: Vaxès fullname: Vaxès, Yann organization: Laboratoire d'Informatique et Systèmes, Aix-Marseille Université and CNRS, Faculté des Sciences de Luminy, F-13288 Marseille, Cedex 9, France |
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| Keywords | Approximation algorithms Hyperbolicity Isometric paths Minimum eccentricity shortest paths |
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| Title | Additive approximation algorithm for geodesic centers in δ-hyperbolic graphs |
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