Abstract
The online median problem consists in finding a sequence of incremental solutions of the k-median problem with k increasing. A particular case of the problem is considered: the clients and facilities are located on the real line. The best algorithm available for the one-dimensional case has competitive ratio 8. We give an improved 5.83-competitive algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. Arya, N. Garg, R. Khandekar, K. Munagala, and V. Pandit, “Local Search Heuristic for k-Median and Facility Location Problems,” in Proceedings of the 33rd Symposium on Theory of Computing (STOC) (ACM Press, New York, 2001), pp. 21–29.
M. Chrobak, C. Kenyon, J. Noga, and N. Young, “Online Medians Via Online Bribery,” arXiv: cs.DS/0504103 (2005) (see http://arxiv.org/abs/cs.DS/0504103).
K. Jain, M. Mahdian, and A. Saberi, “A New Greedy Approach for Facility Location Problems,” in Proceedings of the 34th Symposium on Theory of Computing (STOC) (ACM Press, New York, 2002), pp. 731–740.
R. Mettu and G. Plaxton, “The Online Median Problem,” SIAM J. Comput. 32(3), 816–832 (2003).
Discrete Location Theory, Ed. by P. Mirchandani and R. Francis (Wiley, New York, 1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Shenmaier, 2007, published in Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2007, Vol. 14, No. 2, pp. 95–104.
Rights and permissions
About this article
Cite this article
Shenmaier, V.V. An approximate solution algorithm for the one-dimensional online median problem. J. Appl. Ind. Math. 2, 421–425 (2008). https://doi.org/10.1134/S1990478908030125
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1990478908030125