• Publications
  • Influence
Lectures on discrete geometry
  • J. Matousek
  • Computer Science, Mathematics
  • Graduate texts in mathematics
  • 2 May 2002
TLDR
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. Expand
A subexponential bound for linear programming
TLDR
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. Expand
Reporting Points in Halfspaces
  • J. Matousek
  • Computer Science, Mathematics
  • Comput. Geom.
  • 1 November 1992
TLDR
The halfspace itrange itreporting problem, given a finite set P of points in R d, can be solved substantially more efficiently that the more general simplex range searching problem. Expand
Geometric Discrepancy: An Illustrated Guide
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.Expand
Range searching with efficient hierarchical cuttings
  • J. Matousek
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1 August 1993
TLDR
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. Expand
On linear-time deterministic algorithms for optimization problems in fixed dimension
TLDR
It is shown that with recently developed derandomization techniques, one can convert Clarkson’s randomized algorithm for linear programming in fixed dimension into a linear-time deterministic algorithm, which works in a fairly general abstract setting, which allows us to solve various other problems. Expand
On the complexity of finding iso- and other morphisms for partial k-trees
TLDR
The complexity of these problems when G is restricted to be a partial k -tree is discussed, and a polynomial time algorithm is given for the n disjoint connecting paths problem restricted topartial k -trees (with n part of input). Expand
Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry
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 notExpand
Efficient partition trees
  • J. Matousek
  • Computer Science, Mathematics
  • SCG '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(nExpand
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