TY - GEN

T1 - On the Cycle Augmentation Problem

T2 - 17th International Workshop on Approximation and Online Algorithms, WAOA 2019

AU - Gálvez, Waldo

AU - Grandoni, Fabrizio

AU - Ameli, Afrouz Jabal

AU - Sornat, Krzysztof

N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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 cardinality whose addition to the graph makes it There is an approximation preserving reduction from the mentioned problem to the case (a.k.a. the Tree Augmentation Problem or TAP) or (a.k.a. the Cactus Augmentation Problem or CacAP). While several better-than-2 approximation algorithms are known for TAP, nothing better is known for CacAP (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-hard. In this paper we present a combinatorial approximation for CycAP, for any constant. We also present an LP formulation with a matching integrality gap: this might be useful to address the general case of the problem.

AB - 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 cardinality whose addition to the graph makes it There is an approximation preserving reduction from the mentioned problem to the case (a.k.a. the Tree Augmentation Problem or TAP) or (a.k.a. the Cactus Augmentation Problem or CacAP). While several better-than-2 approximation algorithms are known for TAP, nothing better is known for CacAP (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-hard. In this paper we present a combinatorial approximation for CycAP, for any constant. We also present an LP formulation with a matching integrality gap: this might be useful to address the general case of the problem.

KW - Approximation algorithms

KW - Cactus Augmentation

KW - Connectivity Augmentation

KW - Cycle Augmentation

UR - http://www.scopus.com/inward/record.url?scp=85079539979&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-39479-0_10

DO - 10.1007/978-3-030-39479-0_10

M3 - Conference contribution

AN - SCOPUS:85079539979

SN - 9783030394783

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 138

EP - 153

BT - Approximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers

A2 - Bampis, Evripidis

A2 - Megow, Nicole

PB - Springer

Y2 - 12 September 2019 through 13 September 2019

ER -