TY - JOUR

T1 - Approximating the weight of shallow steiner trees

AU - Kortsarz, Guy

AU - Peleg, David

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

PY - 1999/7/20

Y1 - 1999/7/20

N2 - This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of v vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d ≤ 5. Here we give a polynomial-time approximation algorithm of ratio O(log v) for constant d, which is asymptotically optimal unless P = NP, and an algorithm of ratio O(vε), for any fixed 0 < ε < 1, for general d.

AB - This paper deals with the problem of constructing Steiner trees of minimum weight with diameter bounded by d, spanning a given set of v vertices in a graph. Exact solutions or logarithmic ratio approximation algorithms were known before for the cases of d ≤ 5. Here we give a polynomial-time approximation algorithm of ratio O(log v) for constant d, which is asymptotically optimal unless P = NP, and an algorithm of ratio O(vε), for any fixed 0 < ε < 1, for general d.

UR - http://www.scopus.com/inward/record.url?scp=0037574082&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(99)00111-0

DO - 10.1016/S0166-218X(99)00111-0

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AN - SCOPUS:0037574082

SN - 0166-218X

VL - 93

SP - 265

EP - 285

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 2-3

ER -