Computing autotopism groups of partial Latin rectangles: A pilot study

Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for developing practical software. To this end, we compare six f...

Full description

Bibliographic Details
Authors: Stones, Rebecca J., Falcón Ganfornina, Raúl Manuel, Kotlar, Daniel, Marbach, Trent G.
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2019
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/105208
Online Access:https://hdl.handle.net/11441/105208
https://doi.org/10.1002/cmm4.1094
Access Level:Open access
Keyword:Autotopism
Latin square
Partial Latin rectangle
id ES_6d5d7460f9dbd7e9d06503cecffc5dca
oai_identifier_str oai:idus.us.es:11441/105208
network_acronym_str ES
network_name_str España
repository_id_str
spelling Computing autotopism groups of partial Latin rectangles: A pilot studyStones, Rebecca J.Falcón Ganfornina, Raúl ManuelKotlar, DanielMarbach, Trent G.AutotopismLatin squarePartial Latin rectangleComputing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for developing practical software. To this end, we compare six families of algorithms (two backtracking methods and four graph automorphism methods), with and without the use of entry invariants, on two test suites. We consider two entry invariants: one determined by the frequencies of row, column, and symbol representatives, and one determined by 2 2 submatrices. We nd: (a) with very few entries, many symmetries often exist, and these should be identi ed mathematically rather than computationally, (b) with an intermediate number of entries, a quick-to-compute entry invariant was e ective at reducing the need for computation, (c) with an almost-full partial Latin rectangle, more sophisticated entry invariants are needed, and (d) the performance for (full) Latin squares is signi cantly poorer than other partial Latin rectangles of comparable size, obstructed by the existence of Latin squares with large (possibly transitive) autotopism groups.Junta de Andalucía FQM-016WileyMatemática Aplicada IJunta de Andalucía2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/105208https://doi.org/10.1002/cmm4.1094reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésComputational and Mathematical Methods, Special issue paperFQM-016https://onlinelibrary.wiley.com/doi/full/10.1002/cmm4.1094info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1052082026-06-17T12:51:07Z
dc.title.none.fl_str_mv Computing autotopism groups of partial Latin rectangles: A pilot study
title Computing autotopism groups of partial Latin rectangles: A pilot study
spellingShingle Computing autotopism groups of partial Latin rectangles: A pilot study
Stones, Rebecca J.
Autotopism
Latin square
Partial Latin rectangle
title_short Computing autotopism groups of partial Latin rectangles: A pilot study
title_full Computing autotopism groups of partial Latin rectangles: A pilot study
title_fullStr Computing autotopism groups of partial Latin rectangles: A pilot study
title_full_unstemmed Computing autotopism groups of partial Latin rectangles: A pilot study
title_sort Computing autotopism groups of partial Latin rectangles: A pilot study
dc.creator.none.fl_str_mv Stones, Rebecca J.
Falcón Ganfornina, Raúl Manuel
Kotlar, Daniel
Marbach, Trent G.
author Stones, Rebecca J.
author_facet Stones, Rebecca J.
Falcón Ganfornina, Raúl Manuel
Kotlar, Daniel
Marbach, Trent G.
author_role author
author2 Falcón Ganfornina, Raúl Manuel
Kotlar, Daniel
Marbach, Trent G.
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Junta de Andalucía
dc.subject.none.fl_str_mv Autotopism
Latin square
Partial Latin rectangle
topic Autotopism
Latin square
Partial Latin rectangle
description Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one should have in mind for developing practical software. To this end, we compare six families of algorithms (two backtracking methods and four graph automorphism methods), with and without the use of entry invariants, on two test suites. We consider two entry invariants: one determined by the frequencies of row, column, and symbol representatives, and one determined by 2 2 submatrices. We nd: (a) with very few entries, many symmetries often exist, and these should be identi ed mathematically rather than computationally, (b) with an intermediate number of entries, a quick-to-compute entry invariant was e ective at reducing the need for computation, (c) with an almost-full partial Latin rectangle, more sophisticated entry invariants are needed, and (d) the performance for (full) Latin squares is signi cantly poorer than other partial Latin rectangles of comparable size, obstructed by the existence of Latin squares with large (possibly transitive) autotopism groups.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/105208
https://doi.org/10.1002/cmm4.1094
url https://hdl.handle.net/11441/105208
https://doi.org/10.1002/cmm4.1094
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Computational and Mathematical Methods, Special issue paper
FQM-016
https://onlinelibrary.wiley.com/doi/full/10.1002/cmm4.1094
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869410346666557440
score 15,301603

Similar Items