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An Approximation Algorithm for 2-Vertex-Connectivity via Cycle-Restricted 2-Edge-Covers

Authors Yusuke Kobayashi , Takashi Noguchi

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LIPIcs.ESA.2026.93.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Mathematics of computing → Combinatorial optimization
Keywords
  • approximation algorithm
  • survivable network design
  • minimum 2-vertex-connected spanning subgraph
  • triangle-free 2-matching

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Abstract

In the 2-Vertex-Connected Spanning Subgraph problem (2-VCSS), we are given an undirected graph G, and the objective is to find a 2-vertex-connected spanning subgraph S of G with the minimum number of edges. In the context of survivable network design, 2-VCSS is one of the most fundamental and well-studied problems. There has been active research on improving the approximation ratio of algorithms, and the current best ratio is 4/3, achieved by Bosch-Calvo, Grandoni, and Jabal Ameli. In this paper, we improve the approximation ratio to 95/72+ε (< 1.32). The key idea in our algorithm is to introduce a 2-edge-cover without certain cycle components, and use it as an initial solution.

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Yusuke Kobayashi and Takashi Noguchi. An Approximation Algorithm for 2-Vertex-Connectivity via Cycle-Restricted 2-Edge-Covers. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 93:1-93:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.93

Author Details

Yusuke Kobayashi
  • Research Institute for Mathematical Sciences, Kyoto University, Japan
Takashi Noguchi
  • Research Institute for Mathematical Sciences, Kyoto University, Japan

Funding

This work was partially supported by the joint project of Kyoto University and Toyota Motor Corporation, titled "Advanced Mathematical Science for Mobility Society".
  • Kobayashi, Yusuke: JSPS KAKENHI Grant Numbers JP24K02901, 26K21777. JST ERATO Grant Number JPMJER2301.
  • Noguchi, Takashi: JST SPRING, Grant Number JPMJSP2110.

References

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