Article1978

Finding Two-Centers of a Tree: The Continuous Case

31 citations0/0 files storedTransportation Science

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Facility Location and Emergency Management Complexity and Algorithms in Graphs Computational Geometry and Mesh Generation

Abstract

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 unwariaie single-center problems. The resultant algorithm, whose complexity is a linear function of the number of nodes, requires an additional effort of about 25% over the single-center algorithm to locate an optimal pair of venters. 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.

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References

1964Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph 1973Minimax Location of a Facility in an Undirected Tree Graph 1972Minimax Location of a Facility in a Network 1977The m-Center Problem: Minimax Facility Location 1974A Minimax Location Problem on a Network 1977A Min-Max Theorem for p-Center Problems on a Tree 1971The Optimum Location of Multi-centres on a Graph

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