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
SN - 0041-1655
VL - 12
SP - 93
EP - 106
JO - Transportation Science
JF - Transportation Science
IS - 2
ER -