Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
Planar point location using persistent search trees
Communications of the ACM
Searching and sorting similar lists
Journal of Algorithms
Optimal point location in a monotone subdivision
SIAM Journal on Computing
A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Finding the visibility graph of a simple polygon in time proportional to its size
SCG '87 Proceedings of the third annual symposium on Computational geometry
Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
The complexity of many faces in arrangements of lines of segments
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Recipes for geometry and numerical analysis - Part I: an empirical study
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Towards implementing robust geometric computations
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Arrangements of lines in 3-space: a data structure with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Polynomial real root isolation by differentiation
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
The complexity of elementary algebra and geometry
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An output sensitive algorithm for computing visibility graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Lines in space-combinators, algorithms and applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Counting circular arc intersections
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Computing envelopes in four dimensions with applications
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
Efficient randomized algorithms for some geometric optimization problems
Proceedings of the eleventh annual symposium on Computational geometry
Almost tight upper bounds for vertical decompositions in four dimensions
Journal of the ACM (JACM)
Finding large sticks and potatoes in polygons
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An efficient algorithm for the sign condition problem in the semi-algebraic context
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Efficient evaluation of specific queries in constraint databases
Information Processing Letters
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We show that Collins' classical quantifier elimination procedure contains most of the ingredients for an efficient point location algorithm in higher-dimensional space. This leads to a polynomial-size data structure that allows us to locate, in logarithmic time, a point among a collection of real algebraic varieties of constant maximum degree, assuming that the dimension of the ambient space is fixed. This result has theoretical bearings on a number of optimization problems posed in the literature. It also gives a method for solving multidimensional searching problems in polynomial space and logarithmic query time.