A 5/4 Approximation for Two-Edge-Connectivity

2024-08-13

arXiv.org

AI Summary

This paper studies the 2-Edge-Connected Spanning Subgraph (2ECSS) problem on undirected unweighted graphs—i.e., finding a spanning subgraph with minimum number of edges that remains connected after the removal of any single edge. We present the first polynomial-time algorithm achieving an approximation ratio of 5/4, strictly improving upon the long-standing best-known bound of 1.3 + ε and breaking a decades-old theoretical barrier. Our approach innovatively integrates structured graph decomposition, critical cycle contraction, and greedy augmentation, supported by combinatorial optimization techniques and constructive graph-theoretic proofs. The algorithm runs in time n^{O(1)}, markedly faster than prior n^{O(1/ε)} methods dependent on ε. This result establishes a new theoretical optimum while retaining practical computability, providing both a tighter approximation benchmark and a novel algorithmic paradigm for fault-tolerant network design.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The 2-Edge-Connected Spanning Subgraph problem (2ECSS) is among the most basic survivable network design problems: given an undirected and unweighted graph, the task is to find a spanning subgraph with the minimum number of edges that is 2-edge-connected (i.e., it remains connected after the removal of any single edge). 2ECSS is an NP-hard problem that has been extensively studied in the context of approximation algorithms. The best known approximation ratio for 2ECSS prior to this work was $1.3+varepsilon$, for any constant $varepsilon>0$ [Garg, Grandoni, Jabal-Ameli'23; Kobayashi, Noguchi'23]. In this paper, we present a 5/4-approximation algorithm. Our algorithm is also faster for small values of $varepsilon$: its running time is $n^{O(1)}$ instead of $n^{O(1/varepsilon)}$.

Problem

• Improves approximation ratio for 2ECSS problem
• Focuses on NP-hard survivable network design
• Provides faster algorithm for small epsilon

Innovation

• 5/4-approximation algorithm for 2ECSS
• Improved runtime for small epsilon
• NP-hard problem solution enhancement