Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Data structures for mobile data
Journal of Algorithms
Introduction to Algorithms
Kinetic heap-ordered trees: tight analysis and improved algorithms
Information Processing Letters
Continuous K-Nearest Neighbor Search for Moving Objects
SSDBM '04 Proceedings of the 16th International Conference on Scientific and Statistical Database Management
Continuous K-nearest neighbor queries for continuously moving points with updates
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Continuous range k-nearest neighbor queries in vehicular ad hoc networks
Journal of Systems and Software
Towards a universal tracking database
Proceedings of the 25th International Conference on Scientific and Statistical Database Management
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We consider the problem of evaluating the continuous query of finding the k nearest objects with respect to a given moving point-object Oq among a set of n moving point-objects. The query returns a sequence of answer-pairs, namely pairs of the form (I, S) such that I is a time interval and S is the set of objects that are closest to Oq during I. Existing work on this problem lacks complexity analysis due to limited understanding of the maximum number of answer-pairs. In this paper we analyze the lower bound and the upper bound on the maximum number of answer-pairs. Then we consider two different types of algorithms. The first is off-line algorithms that compute a priori all the answer-pairs. The second type is on-line algorithms that at any time return the current answer-pair. We present the algorithms and analyze their complexity using the maximum number of answer-pairs.