Abstract
We consider the robust 1-center problem on trees with uncertainty in vertex weights and edge lengths. The weights of the vertices and the lengths of the edges can take any value in prespecified intervals with unknown distribution. We show that this problem can be solved in O(n 3 log n) time thus improving on Averbakh and Berman's algorithm with time complexity O(n 6). For the case when the vertices of the tree have weights equal to 1 we show that the robust 1-center problem can be solved in O(nlog n) time, again improving on Averbakh and Berman's time complexity of O(n 2 log n).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Averbakh and O. Berman, Algorithms for the robust 1-center problem on a tree, European Journal of Operational Research 123 (2000) 292-302.
G.N. Frederickson, Parametric search and locating supply centers in trees, in: Algorithms and Data Structures (Ottawa, ON, 1991), Lecture Notes in Computer Science 519 (Springer, Berlin, 1991) pp. 299-319.
G.Y. Handler, Minimax location of a facility in an undirected graph, Transportation Science 7 (1973) 287-293.
N. Megiddo, Linear time algorithms for linear programming in ℝ3 and related problems, SIAM J. Comput. 12 (1983) 759-776.
M. Sharir and P.K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications (Cambridge Univ. Press, New York, 1995).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Burkard, R.E., Dollani, H. A Note on the Robust 1-Center Problem on Trees. Annals of Operations Research 110, 69–82 (2002). https://doi.org/10.1023/A:1020711416254
Issue Date:
DOI: https://doi.org/10.1023/A:1020711416254