Abstract
In this paper we develop some new data structures for storing sets of disks such that different types of queries can be answered efficiently. In particular we study intersection queries with lines and line segments and shooting queries. In the case of non-intersecting disks we obtain structures that use linear storage and have a query time of O(n β+ε+k) for intersection queries, where n is the number of disks, β=log2(1+\(\sqrt 5\)) − 1 ≈ 0.695, ε is an arbitrarily small positive constant, and k is the number of disks reported. For sets of intersecting disks we obtain a structure that uses O(n log n) storage and answers a query in time O(n 2/3log2 n). For ray shooting we obtain a structure that uses linear storage and has O(n β+ε) query time, for any ε>0.KeywordsLine SegmentQuery TimeDisjoint DiskQuery SegmentQuery LineThese 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.
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