Approximation algorithms for facility location problems (extended abstract)
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
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Efficient Algorithm for Minimizing a Sum of p-Norms
SIAM Journal on Optimization
A Newton Acceleration of the Weiszfeld Algorithm forMinimizing the Sum of Euclidean Distances
Computational Optimization and Applications
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
A local search approximation algorithm for k-means clustering
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
A Simple Linear Time (1+ ") -Approximation Algorithm for k-Means Clustering in Any Dimensions
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
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We consider a new problem, which we denote by Continuous Facility Location (ConFL), and its application to the k-Means Problem. Problem ConFL is a natural extension of the Uncapacitated Facility Location Problem where a facility can be any point in Rq. The proposed algorithms are based on a primal-dual technique for spaces with constant dimensions. For the ConFL Problem, we present algorithms with approximation factors 3 + ε and 1.861 + ε for euclidean distances and 9 + ε for squared euclidean distances. For the k-Means Problem (that is restricted to squared euclidean distance), we present an algorithm with approximation factor 54+ ε. All algorithms have good practical behaviour in small dimensions. Comparisons with known algorithms show that the proposed algorithms have good practical behaviour.