Voronoi Trees and Clustering Problems
This paper presents a new data structure called Voronoi tree to support the solution of proximity problems in general pseudo metric spaces with efficiently computable distance functions. We analyse some structural properties and report experimental results showing that Voronoi trees are a proper and very efficient tool for the representation of proximity properties and generation of suitable clusterings.
KeywordsCluster Problem Binary Search Tree Hereditary Property Father Node IEEE Computer Graphic
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- [Dl]F.Dehne: AN O(n4) Algorithm to Construct all Voronoi Diagrams for K Nearest Neighbor Searching in the Euclidean Plane, Proceedings of the 10th International Colloquium on Automata, Languages and Programming (ICALP ’83), Barcelona (Spain), July 18–22, 1983, Lecture Notes in Computer Science, No. 154, Springer 1983Google Scholar
- [D2]F.Dehne: Optical Clustering, Report, Informatik I, Wuerzburg, 1985Google Scholar
- [DJ]Dubes,Jain: Clustering Methodologies in Exploratory Data Analysis, in M.C.Yovits (Ed.): Advances in Computers, Vol.19, Academic Press, 1980Google Scholar
- [DN1]F. Dehne, H. Noltemeier: Clustering Geometric Objects and Applications to Layout Problems, Proceedings Computer Graphics 1985, Tokyo, Springer, Tokyo 1985Google Scholar
- [DN2]F.Dehne, H.Noltemeier: A Computational Geometry Approach to Clustering Problems, Proceedings of the 1st ACM SIGGRAPH Symposium on Computational Geometry, Baltimore, MD, June 5–7, 1985Google Scholar
- [DN3]F.Dehne, H.Noltemeier: Clustering Methods for Geometric Objects and Applications to Design Problems, Report, Informatik I, Wuerzburg 1985, to appear in: IEEE Computer Graphics and Applications, special issue: Computer Graphics Tokyo 85Google Scholar
- [DS]E. Diday, J.C. Simon, Clustering Analysis, in K.S. Fu (ed.), Digital Pattern Recognition, Springer, Berlin, Heidelberg, New York, 1980Google Scholar
- [KMcD]I. Kalantari, G. McDonald: A Data structure and an Algorithm for the Nearest Point Problem, IEEE Transactions on Software Engineering, Vol. SE-9, No.5, Sept.83Google Scholar
- [N]H. Noltemeier: Distances in Hypergraphs, Report, Informatik I, Wuerzburg 1985Google Scholar
- [SH]Shamos, Hoey: Closest Point Problems, Proc. 16th Ann. IEEE Symp. on Found, of Comp. Sci., 1975Google Scholar