Generation of random latin squares step by step and graphically

Autores
Gallego Sagastume, Ignacio
Año de publicación
2014
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
In order to generate random Latin squares of order 256, the Jacobson and Matthews’ algorithm has been implemented in Java. Clear and efficient data structures (for squares and incidence cubes) have been modeled and the ±1-moves of their method have been implemented. This ensures that, in a polynomial number of steps (O(n3)), the algorithm finishes with a Latin square as a result that is approximately uniformly distributed. As an additional contribution to the subject, a step-by-step graphical generation using OpenGL (Open Graphic Library) is provided, which could be used to explain the algorithm, understand it or simply draw the resulting Latin squares as incidence cubes. The main goal of the present work is to document the implementation of the algorithm and make it public on the Internet, since no standard implementation is freely available.
III Workshop de Seguridad Informática (WSI)
Red de Universidades con Carreras de Informática (RedUNCI)
Materia
Ciencias Informáticas
latin squares generation
random
Java implementation
Jacobson Matthews
OpenGL
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/42155

id SEDICI_4506cbc23d01d0bd244cb2fb96bcfcd8
oai_identifier_str oai:sedici.unlp.edu.ar:10915/42155
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Generation of random latin squares step by step and graphicallyGallego Sagastume, IgnacioCiencias Informáticaslatin squares generationrandomJava implementationJacobson MatthewsOpenGLIn order to generate random Latin squares of order 256, the Jacobson and Matthews’ algorithm has been implemented in Java. Clear and efficient data structures (for squares and incidence cubes) have been modeled and the ±1-moves of their method have been implemented. This ensures that, in a polynomial number of steps (O(<i>n</i>3)), the algorithm finishes with a Latin square as a result that is approximately uniformly distributed. As an additional contribution to the subject, a step-by-step graphical generation using OpenGL (Open Graphic Library) is provided, which could be used to explain the algorithm, understand it or simply draw the resulting Latin squares as incidence cubes. The main goal of the present work is to document the implementation of the algorithm and make it public on the Internet, since no standard implementation is freely available.III Workshop de Seguridad Informática (WSI)Red de Universidades con Carreras de Informática (RedUNCI)2014-10info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/42155enginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/ar/Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:01:18Zoai:sedici.unlp.edu.ar:10915/42155Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:01:18.52SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Generation of random latin squares step by step and graphically
title Generation of random latin squares step by step and graphically
spellingShingle Generation of random latin squares step by step and graphically
Gallego Sagastume, Ignacio
Ciencias Informáticas
latin squares generation
random
Java implementation
Jacobson Matthews
OpenGL
title_short Generation of random latin squares step by step and graphically
title_full Generation of random latin squares step by step and graphically
title_fullStr Generation of random latin squares step by step and graphically
title_full_unstemmed Generation of random latin squares step by step and graphically
title_sort Generation of random latin squares step by step and graphically
dc.creator.none.fl_str_mv Gallego Sagastume, Ignacio
author Gallego Sagastume, Ignacio
author_facet Gallego Sagastume, Ignacio
author_role author
dc.subject.none.fl_str_mv Ciencias Informáticas
latin squares generation
random
Java implementation
Jacobson Matthews
OpenGL
topic Ciencias Informáticas
latin squares generation
random
Java implementation
Jacobson Matthews
OpenGL
dc.description.none.fl_txt_mv In order to generate random Latin squares of order 256, the Jacobson and Matthews’ algorithm has been implemented in Java. Clear and efficient data structures (for squares and incidence cubes) have been modeled and the ±1-moves of their method have been implemented. This ensures that, in a polynomial number of steps (O(<i>n</i>3)), the algorithm finishes with a Latin square as a result that is approximately uniformly distributed. As an additional contribution to the subject, a step-by-step graphical generation using OpenGL (Open Graphic Library) is provided, which could be used to explain the algorithm, understand it or simply draw the resulting Latin squares as incidence cubes. The main goal of the present work is to document the implementation of the algorithm and make it public on the Internet, since no standard implementation is freely available.
III Workshop de Seguridad Informática (WSI)
Red de Universidades con Carreras de Informática (RedUNCI)
description In order to generate random Latin squares of order 256, the Jacobson and Matthews’ algorithm has been implemented in Java. Clear and efficient data structures (for squares and incidence cubes) have been modeled and the ±1-moves of their method have been implemented. This ensures that, in a polynomial number of steps (O(<i>n</i>3)), the algorithm finishes with a Latin square as a result that is approximately uniformly distributed. As an additional contribution to the subject, a step-by-step graphical generation using OpenGL (Open Graphic Library) is provided, which could be used to explain the algorithm, understand it or simply draw the resulting Latin squares as incidence cubes. The main goal of the present work is to document the implementation of the algorithm and make it public on the Internet, since no standard implementation is freely available.
publishDate 2014
dc.date.none.fl_str_mv 2014-10
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/publishedVersion
Objeto de conferencia
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
format conferenceObject
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/42155
url http://sedici.unlp.edu.ar/handle/10915/42155
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Argentina (CC BY-NC-SA 2.5)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
_version_ 1844615879667482624
score 13.070432