Space-time tradeoffs for approximate nearest neighbor searching
Journal of the ACM (JACM)
Enclosing weighted points with an almost-unit ball
Information Processing Letters
A unified approach to approximate proximity searching
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximate Halfspace Range Counting
SIAM Journal on Computing
Improved range searching lower bounds
Proceedings of the twenty-eighth annual symposium on Computational geometry
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Range searching is a fundamental problem in computational geometry. The problem involves preprocessing a set of n points in R^d into a data structure, so that it is possible to determine the subset of points lying within a given query range. In approximate range searching, a parameter eps 0 is given, and for a given query range R the points lying within distance eps diam(R) of the range's boundary may be counted or not. In this paper we present three results related to the issue of tradeoffs in approximate range searching. First, we introduce the range sketching problem. Next, we present a space-time tradeoff for smooth convex ranges, which generalize spherical ranges. Finally, we show how to modify the previous data structure to obtain a space-time tradeoff for simplex ranges. In contrast to existing results, which are based on relatively complex data structures, all three of our results are based on simple, practical data structures.