Proximate point searching
نویسندگان
چکیده
In the 2D point searching problem, our goal is to preprocess n points P = {p1, . . . , pn} in the plane so that, for an online sequence of query points q1, . . . qm, we can quickly determine which (if any) of the elements of P are equal to each query point qi. This problem can be solved in O(log n) time by mapping the problem down to one dimension. We present a data structure that is optimized for answering queries quickly when they are geometrically close to the previous successful query. Specifically, our data structure executes queries in time O(log d(qi, qi−1)), where d is some distance metric between two points. Our structure works with a variety of distance metrics. In contrast, we prove that, for some of the most intuitive distance metrics d, it is impossible to obtain an O(log d(qi, qi−1)) runtime, or any bound that is o(log n).
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