Abstract
A c-dop is a c-oriented convex polytope, that is, a convex polytope whose edges have orientations that come from a fixed set of c orientations. In this paper we study dop-trees—bounding-volume hierarchies that use c-dops as bounding volumes—in the plane. We prove that for any set S of n disjoint c-dops in the plane, one can construct a dop-tree such that a range query with a c-dop as query range can be answered in O(n 1/2 + ε + k) time, where k is the number of reported answers. This is optimal up to the factor O(n ε). If the c-dops in S may intersect, the query time becomes O(n \(^{\rm 1-1/{\it c}}\)+k), which is optimal.
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de Berg, M., Haverkort, H., Streppel, M. (2005). Efficient c-Oriented Range Searching with DOP-Trees. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_46
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DOI: https://doi.org/10.1007/11561071_46
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