Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
Halfplanar range search in linear space and O(n0.695) query time
Information Processing Letters
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
SCG '87 Proceedings of the third annual symposium on Computational geometry
Implicitly representing arrangements of lines or segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A deterministic algorithm for partitioning arrangements of lines and its application
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Ray shooting and other applications of spanning trees with low stabbing number
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Space-efficient ray-shooting and intersection searching: algorithms, dynamization, and applications
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Parallel linear programming in fixed dimension almost surely in constant time
Journal of the ACM (JACM)
Almost optimal set covers in finite VC-dimension: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
ACM Computing Surveys (CSUR)
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Range Searching with Delaunay Triangulations
Geoinformatica
On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Approximation algorithms for array partitioning problems
Journal of Algorithms
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Tight bounds for connecting sites across barriers
Proceedings of the twenty-second annual symposium on Computational geometry
Weak visibility of two objects in planar polygonal scenes
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Tight lower bounds for halfspace range searching
Proceedings of the twenty-sixth annual symposium on Computational geometry
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The range searching problems which allow partition trees where every query enters only a sublinear number of nodes are characterized as those with finite Vapnik - Chervonenk is dimension.The concrete combinatorial bounds obtained imply—among others — that every set of n points in the planecan be stored in an &Ogr;(n) space data structure which allows triangle counting queries in &Ogr;(√n· log3n) time, andcan be stored in an &Ogr;(n · log n) space data structure which allows disk counting queries in &Ogr;(√n· log3n) time; the preprocessing time for the data structures is polynomial. Recent results by Chazelle entail that these bounds for space and query time are optimal up to polylog — factors.