TY - JOUR

T1 - FINDING TWO-CENTERS OF A TREE

T2 - THE CONTINUOUS CASE.

AU - Handler, Gabriel Y.

PY - 1978

Y1 - 1978

N2 - An efficient algorithm for finding the absolute single-center (minimax-distance criterion) of a tree is extended to the location of two-centers, where these may be located anywhere on the continuum of points defined by the tree network. A graph-theoretic analysis transforms this bivariate problem into three univariate single-center problems. The resultant algorithm, whose complexity is a linear function of the number of nodes, requires and additional effort of about 25% over the single-center algorithm to locate an optimal par of centers. Two varieties of the problem are considered; in the first, demand for service can occur anywhere on the network; in the second, demand is restricted to the set of nodes.

AB - An efficient algorithm for finding the absolute single-center (minimax-distance criterion) of a tree is extended to the location of two-centers, where these may be located anywhere on the continuum of points defined by the tree network. A graph-theoretic analysis transforms this bivariate problem into three univariate single-center problems. The resultant algorithm, whose complexity is a linear function of the number of nodes, requires and additional effort of about 25% over the single-center algorithm to locate an optimal par of centers. Two varieties of the problem are considered; in the first, demand for service can occur anywhere on the network; in the second, demand is restricted to the set of nodes.

UR - http://www.scopus.com/inward/record.url?scp=0017969599&partnerID=8YFLogxK

U2 - 10.1287/trsc.12.2.93

DO - 10.1287/trsc.12.2.93

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AN - SCOPUS:0017969599

VL - 12

SP - 93

EP - 106

JO - Transportation Science

JF - Transportation Science

SN - 0041-1655

IS - 2

ER -