A note on the p - center problem
DOI:
https://doi.org/10.2298/YJOR1102199JKeywords:
location theory, p - center problemAbstract
The p - center problem is to locate p facilities in a network so as to minimize the longest distance between a demand point and its nearest facility. In this paper, we give a construction on a graph G which produces an infinite ascending chain G=G0≤G1≤G2≤... of graphs containing G such that given any optimal solution X for the p - center problem on G, X is an optimal solution for the p - center problem on i G for any i ≥ 1.References
Bespamyatnikh, S., Bhattacharya, B., Keil, M., Kirkpatrick, D., and Segal, M., “Efficient algorithms for centers and medians in interval and circular-arc graphs”, Networks, 39 (2002) 144-152.
Drezner, Z., and Hamacher, H., Facility Location: Applications and Theory, Springer-Verlag, Berlin, 2002.
Frederickson, G., “Parametric search and locating supply centers in trees”, Proceedings of Workshop on Algorithms and Data Structures, (1991) 299-319.
Goldman, A.J., “Optimal center location in simple networks”, Transportation Science, 5 (1971) 212–221.
Hassin, R., and Tamir, A., “Improved complexity bounds for location problems on the real line”, Operation Research Letters, 10 (1991) 395–402.
Hua, L.K., et al. “Applications of mathematical methods to wheat harvesting”, Chinese Mathematics, 2 (1962) 77–91.
Kariv, O., and Hakimi, S.L., “An algorithmic approach to network location problems. Part I: the p-centers”, SIAM Journal on Applied Mathematics, 37 (1979) 513-538.
Kariv, O., and Hakimi, S.L., “An algorithmic approach to network location problems. Part II: p-medians”, SIAM Journal on Applied Mathematics, 37 (1979) 539–560.
Lan, Y.F., Wang, Y.L., and Suzuki, H., “A linear-time algorithm for solving the center problem on weighted cactus graphs”, Information Processing Letters, 71 (1999) 205-212.
Mirchandani, P.B., and Francis, R., Discrete Location Theory, J.Wiley, 1990.
Tamir, A., “Improved complexity bounds for center location problems on networks by using dynamic data structures”, SIAM Journal of Discrete Mathematics, 1 (1988) 377-396.
West, D.B., Introduction to Graph Theory, 2nd edition, Prentice Hall, USA, 2001.
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