Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Space searching for intersecting objects
Journal of Algorithms
Implicitly representing arrangements of lines or segments
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Partitioning arrangements of lines, part I: an efficient deterministic algorithm
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Quasi-optimal upper bounds for simplex range searching and new zone theorems
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Cutting hyperplane arrangements
Discrete & Computational Geometry
Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Shortest paths among obstacles in the plane
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Vertical decompositions for triangles in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Determining the castability of simple polyhedra
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Almost optimal set covers in finite VC-dimension: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient algorithms for generalized intersection searching on non-iso-oriented objects
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On point location and motion planning among simplices
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On Computing Connected Components of Line Segments
IEEE Transactions on Computers
Sublinear-time approximation of Euclidean minimum spanning tree
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Simplex Range Searching and k Nearest Neighbors of a Line Segment in 2D
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Chromatic distribution of k-nearest neighbors of a line segment in a planar colored point set
Information Processing Letters
Polyline fitting of planar points under min-sum criteria
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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We present an improved space/query time tradeoff for the general simplex range searching problem, matching known lower bounds up to small polylogarithmic factors. In particular, we construct a linear-space simplex range searching data structure with O(n1–1/d) query time, which is optimal for d=2 and probably also for d2. Further we show that multilevel range searching data structures can be built with only a polylogarithmic overhead in space and query time per level (the previous solutions require at least a small fixed power of n). We show that Hopcroft's problem (detecting an incidence among n lines and n points) can be solved in time n4/32O(log n). In all these algorithms, we apply Chazelle's results on computing optimal cuttings.