Abstract
In this paper we consider the problem of locating a path-shaped or tree-shaped (extensive) facility in trees under the condition that existing facilities are already located. We introduce a parametric-pruning method to solve the conditional extensive weighted 1-center location problems in trees in linear time. This improves the recent results of O(n logn) by Tamir et al. [16].
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References
Ben-Moshe, B., Bhattacharya, B., Shi, Q.: An optimal algorithm for the continuous/discrete weighted 2-center problem in trees. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, Springer, Heidelberg (2006)
Bhattacharya, B., Shi, Q.: Optimal algorithms for weighted p-center problem in trees, any fixed p (manuscript, 2006)
Frederickson, G.N.: Parametric search and locating supply centers in trees. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1991. LNCS, vol. 519, pp. 299–319. Springer, Heidelberg (1991)
Frederickson, G.N., Johnson, D.B.: Finding k-th paths and p-centers by generating and searching good data structures. J. of Alg. 4, 61–80 (1983)
Hakimi, S.L.: Optimum location of switching centers and the absolute centers and medians of a graph. Oper. Res. 12, 450–459 (1964)
Hakimi, S.L., Schmeichel, E.F., Labbe, M.: On locating path or tree shaped facilities on networks. Networks 23, 543–555 (1993)
Hedetniemi, S.M., Cockaine, E.J., Hedetniemi, S.T.: Linear algorithms for finding the Jordan center and path center of a tree. Transport. Sci. 15, 98–114 (1981)
Jeger, M., Kariv, O.: Algorithms for finding p-centers on a weighted tree (for relatively small p). Networks 15, 381–389 (1985)
Megiddo, N.: Linear-time algorithms for linear programming in R 3 and related problems. SIAM J. Comput. 12, 759–776 (1983)
Megiddo, N., Tamir, A., Zemel, E., Chandrasekaran, R.: An O(nlog2 n) algorithm for the kth longest path in a tree with applications to location problems. SIAM J. Comput. 10, 328–337 (1981)
Mesa, J.A.: The conditional path center problem in tree graphs, unpublished paper presented to EWGLA8 held in Lambrecht (Germany) (1995)
Minieka, E.: Conditional centers and medians on a graph. Networks 10, 265–272 (1980)
Minieka, E.: The optimal location of a path or tree in a tree network. Networks 15, 309–321 (1985)
Shioura, A., Shigeno, M.: The tree center problems and the relationship with the bottleneck knapsack problems. Networks 29, 107–110 (1997)
Tamir, A., Puerto, J., Pérez-Brito, D.: The centdian subtree on tree networks. Disc. Appl. Math. 118, 263–278 (2002)
Tamir, A., Puerto, J., Mesa, J.A., Rodriguez-Chia, A.M.: Conditional location of path and tree shaped facilities on trees. J. of Alg. 56, 50–75 (2005)
Wang, B.F.: Efficient parallel algorithms for optimally locating a path and a tree of a specified length in a weighted tree network. J. of Alg. 34, 90–108 (2000)
Zemel, E.: An O(n) algorithm for the linear multiple choice knapsack problem and related problems. Information Processing Letters 18, 123–128 (1984)
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Bhattacharya, B., Hu, Y., Shi, Q., Tamir, A. (2006). Optimal Algorithms for the Path/Tree-Shaped Facility Location Problems in Trees. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_39
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DOI: https://doi.org/10.1007/11940128_39
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