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.
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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
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DOI: https://doi.org/10.1007/978-3-642-21204-8_7
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