Halfplanar range search in linear space and O(n0.695) query time
Information Processing Letters
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Line arrangements and range search
Information Processing Letters
Implicitly representing arrangements of lines or segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Geometric transforms for fast geometric algorithms
Geometric transforms for fast geometric algorithms
Intersection queries for curved objects (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A comparative study of efficient algorithms for partitioning a sequence into monotone subsequences
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Tight lower bounds for halfspace range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
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A set A of n points in the plane has to be stored in such a way that for any query triangle t the number of points of A inside t can be computed efficiently. For this problem a solution is presented with &Ogr;(√n log n) query time, &Ogr; (n log n) space and &Ogr;(n3/2 log n) preprocessing time. The constants in the asymptotic bounds are small, and the method is easy to implement.