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 -