Abstract
Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C + q can be retrieved efficiently. If constant time suffices for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the well-known fized radius neighbor problem, to which we thus provide the first known optimal solution.
The first author was supported in part by NSF grant MCS 83-03925.
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Chazelle, B., Edelsbrunner, H. (1985). Optimal solutions for a class of point retrieval problems. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015733
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DOI: https://doi.org/10.1007/BFb0015733
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