Optimal solutions for a class of point retrieval problems
Journal of Symbolic Computation
An Efficient k Nearest Neighbor Searching Algorithm for a Query Line
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Extremal point queries with lines and line segments and related problems
Computational Geometry: Theory and Applications
Computing a closest point to a query hyperplane in three and higher dimensions
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Farthest-Point queries with geometric and combinatorial constraints
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
A simple framework for the generalized nearest neighbor problem
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n),g(n)) if the space requirement for D(X) is O(f) and the 'locate run-time' required for each retrieval is O(g). We show three techniques which can consistently be exploited in solving such problems. For instance, using our techniques, we obtain an O(n2+e, lognlog(l/∈)) spacetime algorithm for the polygon retrieval problem, for arbitrarily small ∈, improving on the previous solution having complexity O(n7,logn).