[图书][B] Triangulations: structures for algorithms and applications

J De Loera, J Rambau, F Santos - 2010 - books.google.com
Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

Abstract order type extension and new results on the rectilinear crossing number

O Aichholzer, H Krasser - Proceedings of the twenty-first annual …, 2005 - dl.acm.org
We extend the order type data base of all realizable order types in the plane to point sets of
cardinality 11. More precisely, we provide a complete data base of all combinatorial different …

Peeling and nibbling the cactus: Subexponential-time algorithms for counting triangulations and related problems

D Marx, T Miltzow - arXiv preprint arXiv:1603.07340, 2016 - arxiv.org
Given a set of $ n $ points $ S $ in the plane, a triangulation $ T $ of $ S $ is a maximal set of
non-crossing segments with endpoints in $ S $. We present an algorithm that computes the …

Counting and enumerating crossing-free geometric graphs

M Wettstein - Proceedings of the thirtieth annual symposium on …, 2014 - dl.acm.org
We describe a framework for counting and enumerating various types of crossing-free
geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and …

A simple aggregative algorithm for counting triangulations of planar point sets and related problems

V Alvarez, R Seidel - Proceedings of the twenty-ninth annual symposium …, 2013 - dl.acm.org
We give an algorithm that determines the number (S) of straight line triangulations of a set S
of n points in the plane in worst case time O (n2 2n). This is the the first algorithm that is …

Counting polygon triangulations is hard

D Eppstein - Discrete & Computational Geometry, 2020 - Springer
Counting Polygon Triangulations is Hard | Discrete & Computational Geometry Skip to main
content SpringerLink Account Menu Find a journal Publish with us Track your research Search …

Counting triangulations and other crossing-free structures via onion layers

V Alvarez, K Bringmann, R Curticapean… - Discrete & Computational …, 2015 - Springer
Let PP be a set of nn points in the plane. A crossing-free structure on PP is a straight-edge
plane graph with vertex set P P. Examples of crossing-free structures include triangulations …

Counting and enumerating pointed pseudotriangulations with the greedy flip algorithm

H Brönnimann, L Kettner, M Pocchiola… - SIAM Journal on …, 2006 - SIAM
We present an algorithm to enumerate the pointed pseudotriangulations of a given point set,
based on the greedy flip algorithm of Pocchiola and Vegter [Discrete Comput. Geom. 16 …

An improved lower bound on the minimum number of triangulations

O Aichholzer, V Alvarez, T Hackl… - … : SoCG'16, June …, 2016 - research-collection.ethz.ch
Upper and lower bounds for the number of geometric graphs of specific types on a given set
of points in the plane have been intensively studied in recent years. For most classes of …

Counting crossing-free structures

V Alvarez, K Bringmann, R Curticapean… - Proceedings of the twenty …, 2012 - dl.acm.org
Let P be a set of n points in the plane. A crossing-free structure on P is a straight-edge
planar graph with vertex set in P. Examples of crossing-free structures include triangulations …