Optimal Time Bounds for Approximate Clustering
Machine Learning
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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The reverse greedy algorithm for the metric k-median problem
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Approximation algorithms for hierarchical location problems
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A distributed O(1)-approximation algorithm for the uniform facility location problem
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Incremental algorithms for facility location and k-Median
Theoretical Computer Science - Approximation and online algorithms
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The Kinetic Facility Location Problem
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An Optimal Incremental Algorithm for Minimizing Lateness with Rejection
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
The reverse greedy algorithm for the metric k-median problem
Information Processing Letters
A Plant Location Guide for the Unsure: Approximation Algorithms for Min-Max Location Problems
Mathematics of Operations Research
Non-cooperative facility location and covering games
Theoretical Computer Science
Randomized priority algorithms
Theoretical Computer Science
Better bounds for incremental medians
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Incremental Facility Location Problem and Its Competitive Algorithms
Journal of Combinatorial Optimization
Better bounds for incremental medians
Theoretical Computer Science
Online and incremental algorithms for facility location
ACM SIGACT News
An experimental evaluation of incremental and hierarchical k-median algorithms
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
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
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
A General Approach for Incremental Approximation and Hierarchical Clustering
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Sampling and Cost-Sharing: Approximation Algorithms for Stochastic Optimization Problems
SIAM Journal on Computing
Facility location in sublinear time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
The reverse greedy algorithm for the metric K-median problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Integration of scheduling and replication in data grids
HiPC'04 Proceedings of the 11th international conference on High Performance Computing
Approximation algorithms for the k-median problem
Efficient Approximation and Online Algorithms
Non-cooperative facility location and covering games
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Oblivious medians via online bidding
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Computing knapsack solutions with cardinality robustness
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Super-fast distributed algorithms for metric facility location
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Deterministic sublinear-time approximations for metric 1-median selection
Information Processing Letters
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We introduce a natural variant of the (metric uncapacitated) k-median problem that we call the online median problem. Whereas the k-median problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the following additional constraints: the facilities are placed one at a time, a facility cannot be moved once it is placed, and the total number of facilities to be placed, k, is not known in advance. The objective of an online median algorithm is to minimize the competitive ratio, that is, the worst-case ratio of the cost of an online placement to that of an optimal offline placement. Our main result is a constant-competitive algorithm for the online median problem running in time that is linear in the input size. In addition, we present a related, though substantially simpler, constant-factor approximation algorithm for the (metric uncapacitated) facility location problem that runs in time linear in the input size. The latter algorithm is similar in spirit to the recent primal-dual-based facility location algorithm of Jain and Vazirani, but our approach is more elementary and yields an improved running time. While our primary focus is on problems which ask us to minimize the weighted average service distance to facilities, we also show that our results can be generalized to hold, to within constant factors, for more general objective functions. For example, we show that all of our approximation results hold, to within constant factors, for the k-means objective function.