TY - JOUR

T1 - Approximating minimum-cost connectivity problems via uncrossable bifamilies

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2012/12

Y1 - 2012/12

N2 - We give approximation algorithms for the Survivable Network problem. The input consists of a graph G = (V, E) with edge/node-costs, a node subset S ⊆ V, and connectivity requirements {r(s, t) : s, t ∈ T ⊆ V}. The goal is to find a minimum cost subgraph H of G that for all s, t ∈ T contains r(s, t) pairwise edge-disjoint st-paths such that no two of them have a node in S \ {s, t} in common. Three extensively studied particular cases are: Edge-Connectivity Survivable Network (S = ∅), Node-Connectivity Survivable Network (S = V), and Element-Connectivity Survivable Network (r(s, t) = 0 whenever s ∈ S or t ∈ S). Let k = maxs,t∈T r(s, t). In Rooted Survivable Network, there is s ∈ T such that r(u, t) = 0 for all u ε= s, and in the Subset k-Connected Subgraph problem r(s, t) = k for all s, t ∈ T.

AB - We give approximation algorithms for the Survivable Network problem. The input consists of a graph G = (V, E) with edge/node-costs, a node subset S ⊆ V, and connectivity requirements {r(s, t) : s, t ∈ T ⊆ V}. The goal is to find a minimum cost subgraph H of G that for all s, t ∈ T contains r(s, t) pairwise edge-disjoint st-paths such that no two of them have a node in S \ {s, t} in common. Three extensively studied particular cases are: Edge-Connectivity Survivable Network (S = ∅), Node-Connectivity Survivable Network (S = V), and Element-Connectivity Survivable Network (r(s, t) = 0 whenever s ∈ S or t ∈ S). Let k = maxs,t∈T r(s, t). In Rooted Survivable Network, there is s ∈ T such that r(u, t) = 0 for all u ε= s, and in the Subset k-Connected Subgraph problem r(s, t) = k for all s, t ∈ T.

UR - http://www.scopus.com/inward/record.url?scp=84872462374&partnerID=8YFLogxK

U2 - 10.1145/2390176.2390177

DO - 10.1145/2390176.2390177

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AN - SCOPUS:84872462374

SN - 1549-6325

VL - 9

JO - ACM Transactions on Algorithms

JF - ACM Transactions on Algorithms

IS - 1

M1 - 1

ER -