### Abstract

Given a data set 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. Reevaluating 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 reevaluation 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 formulas and algorithms for deriving the individual thresholds. Finally, we justify our performance claims with extensive experiments.

Original language | English |
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Article number | 4479463 |

Pages (from-to) | 1205-1216 |

Number of pages | 12 |

Journal | IEEE Transactions on Knowledge and Data Engineering |

Volume | 20 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2008 |

Externally published | Yes |

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### Keywords

- k-means, continuous monitoring, query processing

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Knowledge and Data Engineering*,

*20*(9), 1205-1216. [4479463]. https://doi.org/10.1109/TKDE.2008.54