Local search heuristic for k-median and facility location problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
SIAM Journal on Computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Local Search Heuristics for k-Median and Facility Location Problems
SIAM Journal on Computing
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Competitiveness via primal-dual
ACM SIGACT News
Oblivious medians via online bidding
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Incremental Facility Location Problem and Its Competitive Algorithms
Journal of Combinatorial Optimization
An improved competitive algorithm for one-dimensional incremental median problem
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
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In the incremental version of the well-known k-median problem the objective is to compute 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 R-competitive if the cost of each Fk is at most R times the optimum cost of k facilities. The smallest such R is called the competitive ratio of the sequence {Fk}. Mettu and Plaxton [6,7] presented a polynomial-time algorithm that computes an incremental sequence with competitive ratio ≅ 30. They also showed a lower bound of 2. The upper bound on the ratio was improved to 8 in [5] and [4]. We improve both bounds in this paper. We first show that no incremental sequence can have competitive ratio better than 2.01 and we give a probabilistic construction of a sequence whose competitive ratio is at most 2 + 4√2 ≅ 7.656. We also propose a new approach to the problem that for instances that we refer to as equable achieves an optimal competitive ratio of 2.