Approximate range searching using binary space partitions

M. Berg, de, M.W.A. Streppel

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)

Abstract

We show how any BSP tree for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size for the segments themselves, such that the range-searching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O(nlogn) such that -approximate range searching queries with any constant-complexity convex query range can be answered in O(min>0{(1/)+k}logn) time, where k is the number of segments intersecting the -extended range. The same result can be obtained for disjoint constant-complexity curves, if we allow the BSP to use splitting curves along the given curves. We also describe how to construct a linear-size BSP tree for low-density scenes consisting of n objects in such that -approximate range searching with any constant-complexity convex query range can be done in O(logn+min>0{(1/d-1)+k}) time.
Original languageEnglish
Pages (from-to)139-151
JournalComputational Geometry
Volume33
Issue number3
DOIs
Publication statusPublished - 2006

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