Gálvez, Waldo and Grandoni, Fabrizio and Jabal Ameli, Afrouz and Sornat, Krzysztof (2021) On the Cycle Augmentation Problem: Hardness and Approximation Algorithms. Theory of Computing Systems, 65 (6). pp. 985-1008. ISSN 1432-4350
Full text not available from this repository.Abstract
In the k-Connectivity Augmentation Problem we are given a k-edge-connected graph and a set of additional edges called links. Our goal is to find a set of links of minimum size whose addition to the graph makes it (k + 1)-edge-connected. There is an approximation preserving reduction from the mentioned problem to the case k = 1 (a.k.a. the Tree Augmentation Problem or TAP) or k = 2 (a.k.a. the Cactus Augmentation Problem or CacAP). While several better-than-2 approximation algorithms are known for TAP, for CacAP only recently this barrier was breached (hence for k-Connectivity Augmentation in general). As a first step towards better approximation algorithms for CacAP, we consider the special case where the input cactus consists of a single cycle, the Cycle Augmentation Problem (CycAP). This apparently simple special case retains part of the hardness of the general case. In particular, we are able to show that it is APX-hard. In this paper we present a combinatorial (3/2+ε) -approximation for CycAP, for any constant ε > 0. We also present an LP formulation with a matching integrality gap: this might be useful to address the general case of the problem.
| Item Type: | Scientific journal article, Newspaper article or Magazine article |
|---|---|
| Subjects: | Computer sciences > Computer science > Computational science foundations |
| Department/unit: | Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sull’intelligenza artificiale USI-SUPSI |
| Depositing User: | Fabrizio Grandoni |
| Date Deposited: | 17 Jul 2023 10:03 |
| Last Modified: | 17 Jul 2023 10:09 |
| URI: | http://repository.supsi.ch/id/eprint/14314 |
Actions (login required)
 |
View Item |