TY - JOUR

T1 - A (1 + ln 2) -approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius

AU - Cohen, Nachshon

AU - Nutov, Zeev

PY - 2013/6/10

Y1 - 2013/6/10

N2 - We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in connectivity network design. We give a (1+ln2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem feasible solutions, and on an extension of Steiner Tree technique of Zelikovsky to the Set-Cover problem, which may be of independent interest.

AB - We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in connectivity network design. We give a (1+ln2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem feasible solutions, and on an extension of Steiner Tree technique of Zelikovsky to the Set-Cover problem, which may be of independent interest.

KW - Approximation algorithms

KW - Edge-connectivity

KW - Laminar family

KW - Local replacement

KW - Tree Augmentation

UR - http://www.scopus.com/inward/record.url?scp=84878280922&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2013.04.004

DO - 10.1016/j.tcs.2013.04.004

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AN - SCOPUS:84878280922

SN - 0304-3975

VL - 489-490

SP - 67

EP - 74

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -