Compatible geometric matchings

Authors:
Oswin Aichholzer;Sergey Bereg;Adrian Dumitrescu;Alfredo García;Clemens Huemer;Ferran Hurtado;Mikio Kano;Alberto Márquez;David Rappaport;Shakhar Smorodinsky;Diane Souvaine;Jorge Urrutia;David R. Wood
Affiliations:
Institute for Software Technology, Graz University of Technology, Austria;Department of Computer Science, University of Texas at Dallas, USA;Department of Computer Science, University of Wisconsin-Milwaukee, USA;Departamento de Métodos Estadísticos, Universidad de Zaragoza, Spain;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Spain;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Spain;Department of Computer and Information Sciences, Ibaraki University, Japan;Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain;School of Computing, Queen's University, Canada;Department of Mathematics, Ben-Gurion University, Israel;Department of Computer Science, Tufts University, USA;Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico;Department of Mathematics and Statistics, The University of Melbourne, Australia
Venue:
Computational Geometry: Theory and Applications
Year:
2009

Citing 15
Cited 10

Art gallery theorems and algorithms

Art gallery theorems and algorithms
Computing simple circuits from a set of line segments is NP-complete

SIAM Journal on Computing
Computing simple circuits from a set of line segments

Discrete & Computational Geometry
Hamiltonian triangulations and circumscribing polygons of disjoint line segments

Computational Geometry: Theory and Applications
On a counterexample to a conjecture of Mirzaian

Computational Geometry: Theory and Applications
On circumscribing polygons for line segments

Computational Geometry: Theory and Applications
An orientation theorem with parity conditions

Discrete Applied Mathematics - Special issue on selected papers from First Japanese-Hungarian Symposium for Discrete Mathematics and its Applications
Sequences of spanning trees and a fixed tree theorem

Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Segment endpoint visibility graphs are Hamiltonian

Computational Geometry: Theory and Applications - Special issue on the thirteenth canadian conference on computational geometry - CCCG'01
Alternating paths through disjoint line segments

Information Processing Letters
Pointed and colored binary encompassing trees

SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Graphs of Triangulations and Perfect Matchings

Graphs and Combinatorics
Transforming spanning trees and pseudo-triangulations

Information Processing Letters
Alternating Paths along Axis-Parallel Segments

Graphs and Combinatorics
Augmenting the connectivity of geometric graphs

Computational Geometry: Theory and Applications

Shooting permanent rays among disjoint polygons in the plane

Proceedings of the twenty-fifth annual symposium on Computational geometry
Convex Partitions with 2-Edge Connected Dual Graphs

COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Disjoint compatible geometric matchings

Proceedings of the twenty-seventh annual symposium on Computational geometry
Convex partitions with 2-edge connected dual graphs

Journal of Combinatorial Optimization
Matching points with things

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Non-crossing matchings of points with geometric objects

Computational Geometry: Theory and Applications
Bottleneck non-crossing matching in the plane

ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Bichromatic compatible matchings

Proceedings of the twenty-ninth annual symposium on Computational geometry
Bottleneck non-crossing matching in the plane

Computational Geometry: Theory and Applications
Compatible spanning trees

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect matchings M and M^' of the same set of n points, for some k@?O(logn), there is a sequence of perfect matchings M=M"0,M"1,...,M"k=M^', such that each M"i is compatible with M"i"+"1. This improves the previous best bound of k=