On the Cycle Augmentation Problem: Hardness and Approximation Algorithms

Waldo Gálvez, Fabrizio Grandoni, Afrouz Jabal Ameli, Krzysztof Sornat

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


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.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - 17th International Workshop, WAOA 2019, Revised Selected Papers
EditorsEvripidis Bampis, Nicole Megow
Number of pages16
ISBN (Print)9783030394783
StatePublished - 1 Jan 2020
Externally publishedYes
Event17th International Workshop on Approximation and Online Algorithms, WAOA 2019 - Munich, Germany
Duration: 12 Sep 201913 Sep 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11926 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Workshop on Approximation and Online Algorithms, WAOA 2019


  • Approximation algorithms
  • Cactus Augmentation
  • Connectivity Augmentation
  • Cycle Augmentation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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