e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Approximation algorithms for geometric median problems
Information Processing Letters
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
Incremental clustering and dynamic information retrieval
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Relaxing the Triangle Inequality in Pattern Matching
International Journal of Computer Vision
An improved approximation ratio for the minimum latency problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
K-medians, facility location, and the Chernoff-Wald bound
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
Analysis of a local search heuristic for facility location problems
Journal of 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
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
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
Weak Adversaries for the k-Server Problem
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Multi-processor scheduling to minimize flow time with ε resource augmentation
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Performance guarantees for hierarchical clustering
Journal of Computer and System Sciences - Special issue on COLT 2002
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The reverse greedy algorithm for the metric k-median problem
Information Processing Letters
An Optimal Incremental Algorithm for Minimizing Lateness with Rejection
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Better bounds for incremental medians
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Better bounds for incremental medians
Theoretical Computer Science
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
On hierarchical diameter-clustering, and the supplier problem
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
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Following Mettu and Plaxton [22, 21], we study oblivious algorithms for the k-medians problem. Such an algorithm produces an incremental sequence of facility sets. We give improved algorithms, including a (24+ε)-competitive deterministic polynomial algorithm and a 2e ≈ 5.44-competitive randomized non-polynomial algorithm. Our approach is similar to that of [18], which was done independently. We then consider the competitive ratio with respect to size. An algorithm is s-size-competitive if, for each k, the cost of Fk is at most the minimum cost of any set of k facilities, while the size of Fk is at most sk. We present optimally competitive algorithms for this problem. Our proofs reduce oblivious medians to the following online bidding problem: faced with some unknown threshold $ T \in {\mathbb R}^{+}$, an algorithm must submit “bids” b$\in {\mathbb R}^{+}$ until it submits a bid b ≥ T, paying the sum of its bids. We describe optimally competitive algorithms for online bidding. Some of these results extend to approximately metric distance functions, oblivious fractional medians, and oblivious bicriteria approximation. When the number of medians takes only two possible values k or l, for k l, we show that the optimal cost-competitive ratio is 2 – 1/l.