An improved competitive algorithm for one-dimensional incremental median problem

Authors:
Wenqiang Dai;Yi Feng
Affiliations:
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, Sichuan, P.R. China;School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, Sichuan, P.R. China
Venue:
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Year:
2011

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Abstract

The incremental median problem consists of finding an incremental sequence of facility sets F1 ⊆ F2 ⊆ ... ⊆ Fn, where each Fk contains at most k facilities. We say that this incremental medians sequence is c-competitive if the cost of each Fk 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 + √2)2 ≈ 5.83[19]. In this paper we give an improved polynomial-time algorithm with competitive factor 4.