TY - JOUR

T1 - Approximating multiroot 3-outconnected subgraphs

AU - Nutov, Zeev

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

PY - 2000/10

Y1 - 2000/10

N2 - Consider the following problem: Given an undirected graph with nonnegative edge costs and requirements ku for every node u, find a minimum-cost subgraph that contains max{ku, kv} internally disjoint paths between every pair of nodes u, v. For k = max ku ≥ 2, this problem is NP-hard. The best-known algorithm for it has an approximation ratio of 2(k - 1). For a general instance of the problem, for no value of k ≥ 2, a better approximation algorithm was known. We consider the case of small requirements ku ∈ {1, 2, 3}; these may arise in applications, as, in practical networks, the connectivity requirements are usually rather small. For this case, we give an algorithm with an approximation ratio of 10/3. This improves the best previously known approximation ratio of 4. Our algorithm also implies an improvement for arbitrary k. In the case in which we have an initial graph which is 2-connected, our algorithm achieves an approximation ratio of 2.

AB - Consider the following problem: Given an undirected graph with nonnegative edge costs and requirements ku for every node u, find a minimum-cost subgraph that contains max{ku, kv} internally disjoint paths between every pair of nodes u, v. For k = max ku ≥ 2, this problem is NP-hard. The best-known algorithm for it has an approximation ratio of 2(k - 1). For a general instance of the problem, for no value of k ≥ 2, a better approximation algorithm was known. We consider the case of small requirements ku ∈ {1, 2, 3}; these may arise in applications, as, in practical networks, the connectivity requirements are usually rather small. For this case, we give an algorithm with an approximation ratio of 10/3. This improves the best previously known approximation ratio of 4. Our algorithm also implies an improvement for arbitrary k. In the case in which we have an initial graph which is 2-connected, our algorithm achieves an approximation ratio of 2.

KW - Approximation algorithm

KW - Rooted 3-outconnected subgraph

UR - http://www.scopus.com/inward/record.url?scp=0034288746&partnerID=8YFLogxK

U2 - 10.1002/1097-0037(200010)36:3<172::AID-NET4>3.0.CO;2-P

DO - 10.1002/1097-0037(200010)36:3<172::AID-NET4>3.0.CO;2-P

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AN - SCOPUS:0034288746

SN - 0028-3045

VL - 36

SP - 172

EP - 179

JO - Networks

JF - Networks

IS - 3

ER -