Abstract
Consider two streams of moving objects inside the square [0,1]2. We assume that objects in each of streams move in prescribed manner, but have random coordinate and random time of appearance. One of the streams moves from South to North and we call it a stream of queries, and another stream moves from West to East and we call it a stream of objects. Moving objects closeness problem (MOC problem) consists of enumeration for every new query those and only those objects that will be not far than ρ from the query in Manhattan metrics at some moment of time during the query’s or the objects’ movements inside the square.
In general case this problem is very hard to solve because of dynamic situation and two-dimensional movements of objects and queries. But, in some cases the MOC problem is equivalent to one-dimensional range searching problem that can be solved effectively with logarithmic search, insertion and deletion time and a linear memory size as functions of the number of objects inside the square. In this paper we present and prove criteria for reducibility of the MOC problem to one-dimensional range searching problem.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atallah, M.: Dynamic Computational Geometry. In: Proc. 24th Annu. IEEE Sympos. Found. Comput. Sci. (1983)
Lapshov, I.S.: Dynamic databases with optimal in order time complexity. Discrete Mathematics and Applications 18(4), 367–379 (2006)
Bentley, J.L., Friedman, J.H.: Data structure for range searching. Comput. Surveys 11, 397–409 (1979)
Bolour, A.: Optimal Retrieval Algorithms for Small Regional Queries. SIAM J. Comput. 10, 721–741 (1981)
Bernard, C.: Filtering Search: A new approach to query-answering. SIAM J. Comput (1986)
Fredman, M.L.: A lower bound of complexity of ortogonal range queries. J. ACM 28, 696–705 (1981)
Leuker, G.S.: A data structure for ortogonal range queries. In: Proceedings of 19th Annual IEEE Sympothium on Foundations of Computer Science, pp. 28–34 (1978)
Willard, D.E.: Predicate-oriented database search algorithms. Ph.D. dissertation, Harvard Univ., Cambridge, MA (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Snegova, E. (2010). Criteria for Reducibility of Moving Objects Closeness Problem. In: Catania, B., Ivanović, M., Thalheim, B. (eds) Advances in Databases and Information Systems. ADBIS 2010. Lecture Notes in Computer Science, vol 6295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15576-5_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-15576-5_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15575-8
Online ISBN: 978-3-642-15576-5
eBook Packages: Computer ScienceComputer Science (R0)