The number of small semispaces of a finite set of points in the plane
Noga Alon,E Györi +1 more
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Here it is shown that gk,n = k·n for k n 2 .About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1986-01-01 and is currently open access. It has received 106 citations till now.read more
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Book
Algorithms in Combinatorial Geometry
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
Book
Lectures on Discrete Geometry
TL;DR: 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.
Proceedings ArticleDOI
Applications of random sampling in computational geometry, II
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.
Book
Davenport-Schinzel sequences and their geometric applications
Micha Sharir,Pankaj K. Agarwal +1 more
TL;DR: A close to linear bound on the maximum length of Davenport--Schinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems.
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Geometric Approximation Algorithms
TL;DR: This book is the first to cover geometric approximation algorithms in detail, and topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings.
References
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Journal ArticleDOI
On the Number of Reduced Decompositions of Elements of Coxeter Groups
TL;DR: Using the theory of symmetric functions, a formula is found for r(w) when W is the symmetric group Sn and for the element w0 ∈ Sn of longest length and certain other w ∉ Sn the formula is particularly simple.
Book ChapterDOI
Dissection Graphs of Planar Point Sets
TL;DR: In this paper, the authors discuss the dissection graphs of planar point sets and discuss the general properties of the graphs G k, which can be constructed as follows: any oriented line is to be translated to its left until it meets a point p 1 of S. This line will be called l (0).
Journal ArticleDOI
On the Combinatorial Classification of Nondegenerate Configurations in the Plane
Jacob E. Goodman,Richard Pollack +1 more
TL;DR: It is proved that for n ⩽ 5 every sequence essentially distinct from this one is realized geometrically by giving a complete classification of configurations by developing some basic notions of the geometry of “allowable sequences” in the course of proving this classification theorem.
Journal ArticleDOI
On the Number of k-Subsets of a Set of n Points in the Plane
Jacob E. Goodman,Richard Pollack +1 more
TL;DR: By generalizing to a combinatorial problem, it is shown that for 2 k n the number of sets of size at most k is at most 2 nk − 2 k 2 − k.