e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Incremental clustering and dynamic information retrieval
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Improved approximation algorithms for a capacitated facility location problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
SIAM Journal on Computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the competitive ratio for online facility location
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Better bounds for incremental medians
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
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We consider the incremental version of the k-Facility Location Problem, which is a common generalization of the facility location and the k-median problems. The objective is to produce an incremental sequence of facility sets F 1驴F 2驴驴驴驴驴F n , where each F k contains at most k facilities. An incremental facility sequence or an algorithm producing such a sequence is called c -competitive if the cost of each F k is at most c times the optimum cost of corresponding k-facility location problem, where c is called competitive ratio. In this paper we present two competitive algorithms for this problem. The first algorithm produces competitive ratio 8驴, where 驴 is the approximation ratio of k-facility location problem. By recently result (Zhang, Theor. Comput. Sci. 384:126---135, 2007), we obtain the competitive ratio $16+8\sqrt{3}+\epsilon$ . The second algorithm has the competitive ratio Δ+1, where Δ is the ratio between the maximum and minimum nonzero interpoint distances. The latter result has its self interest, specially for the small metric space with Δ驴8驴驴1.