TY - JOUR

T1 - Fully polynomial approximation schemes for locating a tree-shaped facility

T2 - A generalization of the knapsack problem

AU - Tamir, Arie

PY - 1998/10/5

Y1 - 1998/10/5

N2 - Given an n-node tree T = (V,E), we are concerned with the problem of selecting a subtree of a given length which optimizes the sum of weighted distances of the nodes from the selected subtree. This problem is NP-hard for both the minimization and the maximization versions since it generalizes the knapsack problem. We present fully polynomial approximation schemes which generate a (1 + ε)-approximation and a (1 - ε)-approximation for the minimization and maximization versions respectively, in O(n2/ε) time.

AB - Given an n-node tree T = (V,E), we are concerned with the problem of selecting a subtree of a given length which optimizes the sum of weighted distances of the nodes from the selected subtree. This problem is NP-hard for both the minimization and the maximization versions since it generalizes the knapsack problem. We present fully polynomial approximation schemes which generate a (1 + ε)-approximation and a (1 - ε)-approximation for the minimization and maximization versions respectively, in O(n2/ε) time.

KW - Facility location

KW - Knapsack problems

KW - Tree-shaped facility

UR - http://www.scopus.com/inward/record.url?scp=0042221273&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(98)00059-6

DO - 10.1016/S0166-218X(98)00059-6

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AN - SCOPUS:0042221273

SN - 0166-218X

VL - 87

SP - 229

EP - 243

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1-3

ER -