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Lectures on discrete geometry
- J. Matoušek
- MathematicsGraduate texts in mathematics
- 2 May 2002
This book is primarily a textbook introduction to various areas of discrete geometry, in which several key results and methods are explained, in an accessible and concrete manner, in each area.
Efficient partition trees
- J. Matoušek
- Computer ScienceSCG '91
- 1 June 1991
We prove a theorem on partitioning point sets inEd (d fixed) and give an efficient construction of partition trees based on it. This yields a simplex range searching structure with linear space,O(n…
A subexponential bound for linear programming
- J. Matoušek, M. Sharir, E. Welzl
- Mathematics, Computer ScienceSCG '92
- 1 July 1992
A simple randomized algorithm which solves linear programs withn constraints andd variables in expected time, and computes the lexicographically smallest nonnegative point satisfyingn given linear inequalities ind variables.
Reporting Points in Halfspaces
- J. Matoušek
- Computer Science, MathematicsComputational geometry
- 1 November 1992
Range searching with efficient hierarchical cuttings
- J. Matoušek
- Computer ScienceSCG '92
- 1 July 1992
It is shown 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 ofn) and Hopcroft's problem can be solved in time.
Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry
- J. Matoušek
- Mathematics
- 20 December 2007
A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not…
On variants of the Johnson–Lindenstrauss lemma
- J. Matoušek
- Mathematics, Computer ScienceRandom Struct. Algorithms
- 1 September 2008
A simple and self‐contained proof of a version of the Johnson–Lindenstrauss lemma that subsumes a basic versions by Indyk and Motwani and a version more suitable for efficient computations due to Achlioptas is given.
Geometric Discrepancy: An Illustrated Guide
- J. Matoušek
- Mathematics
- 15 December 2009
1. Introduction 1.1 Discrepancy for Rectangles and Uniform Distribution 1.2 Geometric Discrepancy in a More General Setting 1.3 Combinatorial Discrepancy 1.4 On Applications and Connections 2.…
On the complexity of finding iso- and other morphisms for partial k-trees
- J. Matoušek, R. Thomas
- MathematicsDiscrete Mathematics
- 28 October 1992
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