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Finding Pairwise Intersections Inside a Query Range
<span title="2017-10-31">2017</span>
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We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q . We present data structures of size O ( n · polylog n ) and with query time O ( ( k + 1 ) · polylog n ) time, where k is the number of reported pairs, for two classes of objects in R 2 : axis-aligned rectangles and objects with small union complexity. For the 3-dimensional case where the objects
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... nd the query range are axis-aligned boxes in R 3 , we present a data structure of size O ( n n · polylog n ) and query time O ( ( n + k ) · polylog n ) . When the objects and query are fat, we obtain O ( ( k + 1 ) · polylog n ) query time using O ( n · polylog n ) storage.
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