H. Schipper and M. H. Overmars. Dynamic partition trees. In Scandawian Workshop on Algorithms Theory, volume 2, pages 404--417. Springer-Verlag, 1990. LNCS 447; also to appear in BIT. Home/Search Document Details and Download
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Dynamic Algorithms in Computational Geometry - Chiang, Tamassia (1992) (54 citations) (Correct)
....study lower bounds for the partitions so that many of the proposed partitions are proved to be optimal. The half space range query problem is the following: Given a set of points in R d , and given a query half space, report all the points that lie in the query half space. Schipper and Overmars [143] give a technique for the planar case, by supporting weak deletions on the conjugation tree and then applying the global rebuilding technique of Overmars [121] The resulting technique uses linear space, supports half plane range queries and counting queries in time O(n log 2 (1 p 5) Gamma1 ....
....possibly intersecting) in the plane. Segment intersection queries ask one to report the segments of S intersected by an arbitrary query segment. Ray shooting queries ask one to determine the first segment hit by an arbitrarily directed ray r emanating from a query point q. Schipper and Overmars [143] give a technique for segment intersection queries that works for the case where the segments in S do not intersect each other. They apply the dynamization technique of decomposable searching problem to segment partition trees, and achieve the followsing result: O(n log n) space, O(log 2 n) ....
H. Schipper and M.H. Overmars, "Dynamic Partition Trees," Proc. SWAT'90, Lecture Notes in Computer Science 447 (1990), 404--417.
Geometric Range Searching - Matousek (1994) (40 citations) (Correct)
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H. Schipper and M. H. Overmars. Dynamic partition trees. In Scandawian Workshop on Algorithms Theory, volume 2, pages 404--417. Springer-Verlag, 1990. LNCS 447; also to appear in BIT.
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