TY - JOUR

T1 - A note on Rooted Survivable Networks

AU - Nutov, Zeev

PY - 2009/9/15

Y1 - 2009/9/15

N2 - The (undirected) Rooted Survivable Network Design (Rooted SND) problem is: given a complete graph on node set V with edge-costs, a root s ∈ V, and (node-)connectivity requirements {r (t) : t ∈ T ⊆ V}, find a minimum cost subgraph G that contains r (t) internally-disjoint st-paths for all t ∈ T. For large values of k = maxt ∈ T r (t) Rooted SND is at least as hard to approximate as Directed Steiner Tree [Y. Lando, Z. Nutov, Inapproximability of survivable networks, Theoret. Comput. Sci. 410 (21-23) (2009) 2122-2125]. For Rooted SND, [J. Chuzhoy, S. Khanna, Algorithms for single-source vertex-connectivity, in: FOCS, 2008, pp. 105-114] gave recently an approximation algorithm with ratio O (k2 log n). Independently, and using different techniques, we obtained at the same time a simpler primal-dual algorithm with the same ratio.

AB - The (undirected) Rooted Survivable Network Design (Rooted SND) problem is: given a complete graph on node set V with edge-costs, a root s ∈ V, and (node-)connectivity requirements {r (t) : t ∈ T ⊆ V}, find a minimum cost subgraph G that contains r (t) internally-disjoint st-paths for all t ∈ T. For large values of k = maxt ∈ T r (t) Rooted SND is at least as hard to approximate as Directed Steiner Tree [Y. Lando, Z. Nutov, Inapproximability of survivable networks, Theoret. Comput. Sci. 410 (21-23) (2009) 2122-2125]. For Rooted SND, [J. Chuzhoy, S. Khanna, Algorithms for single-source vertex-connectivity, in: FOCS, 2008, pp. 105-114] gave recently an approximation algorithm with ratio O (k2 log n). Independently, and using different techniques, we obtained at the same time a simpler primal-dual algorithm with the same ratio.

KW - Approximation algorithms

KW - Network design

KW - Rooted node-connectivity

UR - http://www.scopus.com/inward/record.url?scp=69249215157&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2009.07.011

DO - 10.1016/j.ipl.2009.07.011

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AN - SCOPUS:69249215157

SN - 0020-0190

VL - 109

SP - 1114

EP - 1119

JO - Information Processing Letters

JF - Information Processing Letters

IS - 19

ER -