Abstract
The incremental median problem consists of finding an incremental sequence of facility sets F 1 ⊆ F 2 ⊆ ⋯ ⊆ F n , where each F k contains at most k facilities. We say that this incremental medians sequence is c-competitive if the cost of each F k is at most c times of the optimum cost of k-median problem. The smallest such c is called the competitive ratio. A particular case of the problem is considered in this paper: both the clients and facilities are located on the real line. [5] and [14] presented a polynomial-time algorithm for this one-dimensional case that computes an incremental sequence with competitive ratio 8. The best algorithm available has competitive ratio \((1+\sqrt{2})^2\approx 5.83\)[19]. In this paper we give an improved polynomial-time algorithm with competitive factor 4.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arora, S., Raghavan, P., Rao, S.: Approximation schemes for Euclidean k-medians and related problems. In: STOC 1998, pp. 106–113 (1998)
Arya, V., Garg, N., Khandekar, R., Munagala, K., Pandit, V.: Local search heuristics for k-median and facility location problems. In: STOC 2001, pp. 21–29 (2001)
Brandeau, M.L., Chiu, S.S.: An overview of representative problems in location research. Management Science 35(6), 645–674 (1989)
Chrobak, M., Hurand, M.: Better bounds for incremental medians. In: Kaklamanis, C., Skutella, M. (eds.) WAOA 2007. LNCS, vol. 4927, pp. 207–217. Springer, Heidelberg (2008)
Chrobak, M., Kenyon, C., Young, N.E.: Oblivious medians via online bidding. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 311–322. Springer, Heidelberg (2006)
Daskin, M. (ed.): Network and Discrete Location. Wiley, New York (1995)
Drezner, Z. (ed.): Facility Location: A Survey of Applications and Methods. Springer, New York (1995)
Drezner, Z., Hamacher, H. (eds.): Facility Location: Applications and Theory. Springer, Berlin (2002)
Goldman, A.J.: Optimal center location in simple networks. Transportation Science 5, 212–221 (1971)
Goldman, A.J., Witzgall, C.J.: A localization theorem for optimal facility location. Transportation Science 4, 406–409 (1970)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)
Hassin, R., Tamir, A.: Improved complexity bounds for location problems on the real line. Operations Research Letters 10, 395–402 (1991)
Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: STOC 2002, pp. 731–740 (2002)
Lin., G.L., Nagarajan, C., Rajamaran, R., Williamson, D.P.: A general approach for incremental approximation and hierarchical clustering. In: SODA 2002. ACM/SIAM (2006)
Lin, J.H., Vitter, J.S.: ε-approximations with minimum packing constraint violation. In: STOC 1992, pp. 771–782 (1992)
Love, R.F., Morris, J.G., Wesolowsky, G.O. (eds.): Facilities Location: Models and Methods. North Holland, New York (1988)
Mettu, R.R., Plaxton, C.G.: The online median problem. SIAM Journal of Computing 32(3), 816–832 (2003)
Mirchandani, P., Francis, R. (eds.): Discrete location theory. Wiley Interscience, Hoboken (1990)
Shenmaier, V.V.: An Approximate Solution Algorithm for the One-Dimensional Online Median Problem. Journal of Applied and Industrial Mathematics 2(3), 421–425 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dai, W., Feng, Y. (2011). An Improved Competitive Algorithm for One-Dimensional Incremental Median Problem. In: Atallah, M., Li, XY., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 6681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21204-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-21204-8_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21203-1
Online ISBN: 978-3-642-21204-8
eBook Packages: Computer ScienceComputer Science (R0)