Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
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
How Fast Is the k-Means Method?
Algorithmica
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
How slow is the k-means method?
Proceedings of the twenty-second annual symposium on Computational geometry
Worst-case and Smoothed Analysis of the ICP Algorithm, with an Application to the k-means Method
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Improved smoothed analysis of the k-means method
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Adaptive Sampling for k-Means Clustering
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Worst-Case and Smoothed Analysis of k-Means Clustering with Bregman Divergences
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Local search: simple, successful, but sometimes sluggish
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Bregman clustering for separable instances
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
On the power of nodes of degree four in the local max-cut problem
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
StreamKM++: A clustering algorithm for data streams
Journal of Experimental Algorithmics (JEA)
Multidirectional knowledge extraction process for creating behavioral personas
Proceedings of the 10th Brazilian Symposium on on Human Factors in Computing Systems and the 5th Latin American Conference on Human-Computer Interaction
Adaptive key frame extraction for video summarization using an aggregation mechanism
Journal of Visual Communication and Image Representation
Size Constrained Distance Clustering: Separation Properties and Some Complexity Results
Fundamenta Informaticae - From Physics to Computer Science: to Gianpiero Cattaneo for his 70th birthday
Prediction of atomic web services reliability based on k-means clustering
Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering
Data stream clustering: A survey
ACM Computing Surveys (CSUR)
Optimising sum-of-squares measures for clustering multisets defined over a metric space
Discrete Applied Mathematics
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The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its running time (i.e. O(nkd)) is, in general, exponential in the number of points (when kd=Ω(n log n)). Recently, Arthur and Vassilvitskii [2] showed a super-polynomial worst-case analysis, improving the best known lower bound from Ω(n) to 2Ω(√n) with a construction in d=Ω(√n) dimensions. In [2] they also conjectured the existence of super-polynomial lower bounds for any d≥ 2. Our contribution is twofold: we prove this conjecture and we improve the lower bound, by presenting a simple construction in the plane that leads to the exponential lower bound 2Ω(n).