Matching points with circles and squares

Bernardo M. Ábrego; Esther M. Arkin; Silvia Fernández-Merchant; Ferran Hurtado; Mikio Kano; Joseph S.B. Mitchell; Jorge Urrutia

doi:10.1007/11589440_1

Matching points with circles and squares

Bernardo M. Ábrego
, Esther M. Arkin
, Silvia Fernández-Merchant
, Ferran Hurtado
, Mikio Kano
, Joseph S.B. Mitchell
, Jorge Urrutia

Applied Mathematics and Statistics

California State University Northridge
Polytechnic University of Catalonia
Ibaraki University
Universidad Nacional Autónoma de México

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

Given a class C of geometric objects and a point set P, a C-matching of P is a set M = {C₁, . . . ,C_k} of elements of C such that each C_i contains exactly two elements of P. If all of the elements of P belong to some C_i, M is called a perfect matching; if in addition all the elements of M are pairwise disjoint we say that this matching M is strong. In this paper we study the existence and properties of C-matchings for point sets in the plane when C is the set of circles or the set of isothetic squares in the plane.

Original language	English
Title of host publication	Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers
Publisher	Springer Verlag
Pages	1-15
Number of pages	15
ISBN (Print)	3540304673, 9783540304678
DOIs	https://doi.org/10.1007/11589440_1
State	Published - 2005
Event	Japanese Conference on Discrete and Computational Geometry, JCDCG 2004 - Tokyo, Japan Duration: Oct 8 2004 → Oct 11 2004

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3742 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Japanese Conference on Discrete and Computational Geometry, JCDCG 2004
Country/Territory	Japan
City	Tokyo
Period	10/8/04 → 10/11/04

Access to Document

10.1007/11589440_1

Cite this

Ábrego, B. M., Arkin, E. M., Fernández-Merchant, S., Hurtado, F., Kano, M., Mitchell, J. S. B., & Urrutia, J. (2005). Matching points with circles and squares. In Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers (pp. 1-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3742 LNCS). Springer Verlag. https://doi.org/10.1007/11589440_1

Ábrego, Bernardo M. ; Arkin, Esther M. ; Fernández-Merchant, Silvia et al. / Matching points with circles and squares. Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers. Springer Verlag, 2005. pp. 1-15 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{38ea6ebe23a44cfb97d8fc336f214058,

title = "Matching points with circles and squares",

abstract = "Given a class C of geometric objects and a point set P, a C-matching of P is a set M = \{C1, . . . ,Ck\} of elements of C such that each Ci contains exactly two elements of P. If all of the elements of P belong to some Ci, M is called a perfect matching; if in addition all the elements of M are pairwise disjoint we say that this matching M is strong. In this paper we study the existence and properties of C-matchings for point sets in the plane when C is the set of circles or the set of isothetic squares in the plane.",

author = "{\'A}brego, \{Bernardo M.\} and Arkin, \{Esther M.\} and Silvia Fern{\'a}ndez-Merchant and Ferran Hurtado and Mikio Kano and Mitchell, \{Joseph S.B.\} and Jorge Urrutia",

year = "2005",

doi = "10.1007/11589440\_1",

language = "English",

isbn = "3540304673",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "1--15",

booktitle = "Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers",

note = "Japanese Conference on Discrete and Computational Geometry, JCDCG 2004 ; Conference date: 08-10-2004 Through 11-10-2004",

}

Ábrego, BM, Arkin, EM, Fernández-Merchant, S, Hurtado, F, Kano, M, Mitchell, JSB & Urrutia, J 2005, Matching points with circles and squares. in Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3742 LNCS, Springer Verlag, pp. 1-15, Japanese Conference on Discrete and Computational Geometry, JCDCG 2004, Tokyo, Japan, 10/8/04. https://doi.org/10.1007/11589440_1

Matching points with circles and squares. / Ábrego, Bernardo M.; Arkin, Esther M.; Fernández-Merchant, Silvia et al.
Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers. Springer Verlag, 2005. p. 1-15 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3742 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Matching points with circles and squares

AU - Ábrego, Bernardo M.

AU - Arkin, Esther M.

AU - Fernández-Merchant, Silvia

AU - Hurtado, Ferran

AU - Kano, Mikio

AU - Mitchell, Joseph S.B.

AU - Urrutia, Jorge

PY - 2005

Y1 - 2005

N2 - Given a class C of geometric objects and a point set P, a C-matching of P is a set M = {C1, . . . ,Ck} of elements of C such that each Ci contains exactly two elements of P. If all of the elements of P belong to some Ci, M is called a perfect matching; if in addition all the elements of M are pairwise disjoint we say that this matching M is strong. In this paper we study the existence and properties of C-matchings for point sets in the plane when C is the set of circles or the set of isothetic squares in the plane.

AB - Given a class C of geometric objects and a point set P, a C-matching of P is a set M = {C1, . . . ,Ck} of elements of C such that each Ci contains exactly two elements of P. If all of the elements of P belong to some Ci, M is called a perfect matching; if in addition all the elements of M are pairwise disjoint we say that this matching M is strong. In this paper we study the existence and properties of C-matchings for point sets in the plane when C is the set of circles or the set of isothetic squares in the plane.

UR - https://www.scopus.com/pages/publications/33646504690

U2 - 10.1007/11589440_1

DO - 10.1007/11589440_1

M3 - Conference contribution

AN - SCOPUS:33646504690

SN - 3540304673

SN - 9783540304678

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 15

BT - Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers

PB - Springer Verlag

T2 - Japanese Conference on Discrete and Computational Geometry, JCDCG 2004

Y2 - 8 October 2004 through 11 October 2004

ER -

Ábrego BM, Arkin EM, Fernández-Merchant S, Hurtado F, Kano M, Mitchell JSB et al. Matching points with circles and squares. In Discrete and Computational Geometry - Japanese Conference, JCDCG 2004, Revised Selected Papers. Springer Verlag. 2005. p. 1-15. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11589440_1

Matching points with circles and squares

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