TY - JOUR

T1 - A 2-Approximation Algorithm for Finding an Optimum 3-Vertex-Connected Spanning Subgraph

AU - Auletta, Vincenzo

AU - Dinitz, Yefim

AU - Nutov, Zeev

AU - Parente, Domenico

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. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there exist k internally vertex-disjoint paths to every other vertex), we derive polynomial time algorithm for finding a ([k/2] + 1)-connected subgraph with a weight at most twice the optimum to the original problem. In particular, we obtain a 2-approximation algorithm for the case k = 3 of our problem. This improves the best previously known approximation ratio 3. The complexity of the algorithm is O(|V|3|E|) = O(|V|5).

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. Combining properties of inclusion-minimal k-vertex connected graphs and of k-out-connected graphs (i.e., graphs which contain a vertex from which there exist k internally vertex-disjoint paths to every other vertex), we derive polynomial time algorithm for finding a ([k/2] + 1)-connected subgraph with a weight at most twice the optimum to the original problem. In particular, we obtain a 2-approximation algorithm for the case k = 3 of our problem. This improves the best previously known approximation ratio 3. The complexity of the algorithm is O(|V|3|E|) = O(|V|5).

UR - http://www.scopus.com/inward/record.url?scp=0001977155&partnerID=8YFLogxK

U2 - 10.1006/jagm.1999.1006

DO - 10.1006/jagm.1999.1006

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AN - SCOPUS:0001977155

SN - 0196-6774

VL - 32

SP - 21

EP - 30

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 1

ER -