论文信息 - The continuous m-center problem on a network

The continuous m-center problem on a network

In the continuous m-center problem on a network, m-centers are to be located along the arcs of the network so as to minimize the maximum (shortest) distance from any point on the network to a nearest center. The typical application scenario is to the location of emergency facilities in a transportation network. In this article, we propose a solution procedure for this hitherto unsolved problem. The procedure is a relaxation algorithm which may be viewed as a column and row generating procedure for the infinite size covering problems needed to solve the problem. The optimum-seeking procedure is expected to be practical for large-scale networks.

Gabriel Y. Handler | Margalit Rozman | G. Handler | Margalit Rozman

[1] Timothy J. Lowe,et al. Location on Networks: A Survey. Part I: The p-Center and p-Median Problems , 1983 .

[2] O. Kariv,et al. An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[3] G. Handler. Minimax Location of a Facility in an Undirected Tree Graph , 1973 .

[4] E. Minieka. The m-Center Problem , 1970 .

[5] Pitu B. Mirchandani,et al. Location on networks : theory and algorithms , 1979 .

[6] Edward Minieka,et al. The Centers and Medians of a Graph , 1977, Oper. Res..

[7] S. L. Hakimi,et al. Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[8] Andrew C. Ho,et al. Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study , 1980 .

[9] E. Balas. Cutting planes from conditional bounds: A new approach to set covering , 1980 .

[10] Gabriel Y. Handler,et al. Finding Two-Centers of a Tree: The Continuous Case , 1978 .

[11] Arie Tamir,et al. An O ((nlog p)2) Algorithm for the Continuous p-Center Problem on a Tree , 1980, SIAM J. Matrix Anal. Appl..

[12] H. Frank,et al. Letter to the Editor - A Note on a Graph Theoretic Game of Hakimi's , 1967, Oper. Res..

[13] Nicos Christofides,et al. Note—A Computational Survey of Methods for the Set Covering Problem , 1975 .