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An Approximation Algorithm for Two-Edge-Connected Subgraph Problem via Triangle-Free Two-Edge-Cover

Authors Yusuke Kobayashi , Takashi Noguchi

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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", and by JSPS KAKENHI Grant Numbers JP20K11692 and JP22H05001.

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Yusuke Kobayashi and Takashi Noguchi. An Approximation Algorithm for Two-Edge-Connected Subgraph Problem via Triangle-Free Two-Edge-Cover. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 49:1-49:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.49

Abstract

The 2-Edge-Connected Spanning Subgraph problem (2-ECSS) is one of the most fundamental and well-studied problems in the context of network design. We are given an undirected graph G, and the objective is to find a 2-edge-connected spanning subgraph H of G with the minimum number of edges. For this problem, a lot of approximation algorithms have been proposed in the literature. In particular, very recently, Garg, Grandoni, and Ameli gave an approximation algorithm for 2-ECSS with a factor of 1.326, which is the best approximation ratio. In this paper, under the assumption that a maximum triangle-free 2-matching can be found in polynomial time in a graph, we give a (1.3+ε)-approximation algorithm for 2-ECSS, where ε is an arbitrarily small positive fixed constant. Note that a complicated polynomial-time algorithm for finding a maximum triangle-free 2-matching is announced by Hartvigsen in his PhD thesis, but it has not been peer-reviewed or checked in any other way. In our algorithm, we compute a minimum triangle-free 2-edge-cover in G with the aid of the algorithm for finding a maximum triangle-free 2-matching. Then, with the obtained triangle-free 2-edge-cover, we apply the arguments by Garg, Grandoni, and Ameli.

Subject Classification

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

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