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Issue No. 09 - September (2008 vol. 20)
ISSN: 1041-4347
pp: 1205-1216
Zhenjie Zhang , NUS, Singapore
Yin Yang , Hong Kong University of Science and Technology, Hong Kong
Anthony K.H. Tung , National University of Singapore NUS, Singapore Singapore
Dimitris Papadias , Hong Kong University of Science and Technology, Hong Kong
Given a dataset P, a k-means query returns k points in space (called centers), such that the average squared distance between each point in P and its nearest center is minimized. Since this problem is NP-hard, several approximate algorithms have been proposed and used in practice. In this paper, we study continuous k-means computation at a server that monitors a set of moving objects. Re-evaluating k-means every time there is an object update imposes a heavy burden on the server (for computing the centers from scratch) and the clients (for continuously sending location updates). We overcome these problems with a novel approach that significantly reduces the computation and communication costs, while guaranteeing that the quality of the solution, with respect to the re-evaluation approach, is bounded by a user-defined tolerance. The proposed method assigns each moving object a threshold (i.e., range) such that the object sends a location update only when it crosses the range boundary. First, we develop an efficient technique for maintaining the k-means. Then, we present mathematical formulae and algorithms for deriving the individual thresholds. Finally, we justify our performance claims with extensive experiments.
Data mining, Spatial databases and GIS

D. Papadias, Y. Yang, A. K. Tung and Z. Zhang, "Continuous k-Means Monitoring over Moving Objects," in IEEE Transactions on Knowledge & Data Engineering, vol. 20, no. , pp. 1205-1216, 2008.
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