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A 4/3 Approximation for 2-Vertex-Connectivity

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

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Author Details

Miguel Bosch-Calvo
  • IDSIA, USI-SUPSI, Lugano, Switzerland
Fabrizio Grandoni
  • IDSIA, USI-SUPSI, Lugano, Switzerland
Afrouz Jabal Ameli
  • TU Eindhoven, The Netherlands

Funding

The first 2 authors are partially supported by the SNF Grant 200021_200731 / 1.

Cite AsGet BibTex

Miguel Bosch-Calvo, Fabrizio Grandoni, and Afrouz Jabal Ameli. A 4/3 Approximation for 2-Vertex-Connectivity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.29

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Algorithm
  • Network Design
  • Vertex-Connectivity
  • Approximation

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