License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.29
URN: urn:nbn:de:0030-drops-180813
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18081/
Go to the corresponding LIPIcs Volume Portal

Bosch-Calvo, Miguel ; Grandoni, Fabrizio ; Jabal Ameli, Afrouz

A 4/3 Approximation for 2-Vertex-Connectivity

pdf-format:
LIPIcs-ICALP-2023-29.pdf (0.7 MB)

Abstract

The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph G. Our goal is to find a subgraph S of G with the minimum number of edges which is 2-vertex-connected, namely S remains connected after the deletion of an arbitrary node. 2VCSS is well-studied in terms of approximation algorithms, and the current best (polynomial-time) approximation factor is 10/7 by Heeger and Vygen [SIDMA'17] (improving on earlier results by Khuller and Vishkin [STOC'92] and Garg, Vempala and Singla [SODA'93]).
Here we present an improved 4/3 approximation. Our main technical ingredient is an approximation preserving reduction to a conveniently structured subset of instances which are "almost" 3-vertex-connected. The latter reduction might be helpful in future work.

BibTeX - Entry

@InProceedings{boschcalvo_et_al:LIPIcs.ICALP.2023.29,
  author =	{Bosch-Calvo, Miguel and Grandoni, Fabrizio and Jabal Ameli, Afrouz},
  title =	{{A 4/3 Approximation for 2-Vertex-Connectivity}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{29:1--29:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18081},
  URN =		{urn:nbn:de:0030-drops-180813},
  doi =		{10.4230/LIPIcs.ICALP.2023.29},
  annote =	{Keywords: Algorithm, Network Design, Vertex-Connectivity, Approximation}
}

Keywords: Algorithm, Network Design, Vertex-Connectivity, Approximation
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI