TY - JOUR

T1 - A 3-Approximation Algorithm for Finding Optimum 4,5-Vertex-Connected Spanning Subgraphs

AU - Dinitz, Yefim

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1999/7

Y1 - 1999/7

N2 - The problem of finding a minimum weight k-vertex connected spanning subgraph in a graph G = (V, E) is considered. For k ≥ 2, this problem is known to be NP-hard. Based on the paper of Auletta, Dinitz, Nutov, and Parente in this issue, we derive a 3-approximation algorithm for k ∈ {4,5}. This improves the best previously known approximation ratios 41/6 and 417/30, respectively. The complexity of the suggested algorithm is O(|V|5) for the deterministic and O(\V\4log|V|) for the randomized version. The way of solution is as follows. Analyzing a subgraph constructed by the algorithm of the aforementioned paper, we prove that all its "small" cuts have exactly two sides and separate a certain fixed pair of vertices. Such a subgraph is augmented to a k-connected one (optimally) by at most four executions of a min-cost k-flow algorithm.

AB - The problem of finding a minimum weight k-vertex connected spanning subgraph in a graph G = (V, E) is considered. For k ≥ 2, this problem is known to be NP-hard. Based on the paper of Auletta, Dinitz, Nutov, and Parente in this issue, we derive a 3-approximation algorithm for k ∈ {4,5}. This improves the best previously known approximation ratios 41/6 and 417/30, respectively. The complexity of the suggested algorithm is O(|V|5) for the deterministic and O(\V\4log|V|) for the randomized version. The way of solution is as follows. Analyzing a subgraph constructed by the algorithm of the aforementioned paper, we prove that all its "small" cuts have exactly two sides and separate a certain fixed pair of vertices. Such a subgraph is augmented to a k-connected one (optimally) by at most four executions of a min-cost k-flow algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0002512902&partnerID=8YFLogxK

U2 - 10.1006/jagm.1999.1007

DO - 10.1006/jagm.1999.1007

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AN - SCOPUS:0002512902

SN - 0196-6774

VL - 32

SP - 31

EP - 40

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 1

ER -