An Approximation Algorithm for 2-Vertex-Connectivity via Cycle-Restricted 2-Edge-Covers
2026-05-11 • Data Structures and Algorithms
Data Structures and Algorithms
AI summaryⓘ
The authors study a problem where one needs to find a smaller sub-network of an existing network that remains connected even if one node fails, using as few connections as possible. They improve on previous methods by finding a new better way to approximate this minimal sub-network, lowering the ratio from 4/3 to about 1.32. Their approach involves starting with a special kind of sub-network that covers all edges but avoids certain cycle structures, which helps in building a more efficient solution.
2-vertex-connected spanning subgraphapproximation algorithmsurvivable network design2-edge-covergraph connectivityspanning subgraphcycle componentsapproximation ratio
Authors
Yusuke Kobayashi, Takashi Noguchi
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 $\frac{4}{3}$, achieved by Bosch-Calvo, Grandoni, and Jabal Ameli. In this paper, we improve the approximation ratio to $\frac{95}{72}+\varepsilon$ ($<1.32$). The key idea in our algorithm is to introduce a 2-edge-cover without certain cycle components, and use it as an initial solution.