An Integer Linear Programming Model for Tilings

In this paper, we propose an Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how this model can be used to efficiently check the necessity of the Coven-Meyerowitz's \((T2)\) condition and also to define an iterative algorithm that finds all t...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Auricchio, Gennaro, Ferrarini, Luca, Lanzarotto, Greta
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.07.2021
Subjects
Integer programming
Iterative algorithms
Iterative methods
Linear programming
Rhythm
Tiling
Online AccessGet full text

Cover

Abstract In this paper, we propose an Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how this model can be used to efficiently check the necessity of the Coven-Meyerowitz's \((T2)\) condition and also to define an iterative algorithm that finds all the possible tilings of the rhythm A. To conclude, we run several experiments to validate the time efficiency of this model.
AbstractList In this paper, we propose an Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how this model can be used to efficiently check the necessity of the Coven-Meyerowitz's \((T2)\) condition and also to define an iterative algorithm that finds all the possible tilings of the rhythm A. To conclude, we run several experiments to validate the time efficiency of this model.
Author Ferrarini, Luca
Auricchio, Gennaro
Lanzarotto, Greta
Author_xml – sequence: 1
  givenname: Gennaro
  surname: Auricchio
  fullname: Auricchio, Gennaro
– sequence: 2
  givenname: Luca
  surname: Ferrarini
  fullname: Ferrarini, Luca
– sequence: 3
  givenname: Greta
  surname: Lanzarotto
  fullname: Lanzarotto, Greta
BookMark eNrjYmDJy89LZWLgNDI2NtS1MDEy4mDgLS7OMjAwMDIzNzI1NeZk0HfMU_DMK0lNTy1S8MnMS00sUggoyk8vSszNzcxLV_DNT0nNUUjLL1IIycwBChTzMLCmJeYUp_JCaW4GZTfXEGcP3YKi_MLS1OKS-Kz80qI8oFQ80AIDE3NLSyNTY-JUAQAbhTP_
ContentType Paper
Copyright 2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
PTHSS
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Database (Proquest)
ProQuest Central (Alumni)
ProQuest Central
ProQuest Central Essentials
AUTh Library subscriptions: ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
Publicly Available Content Database
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest One Academic
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-proquest_journals_25504799253
IEDL.DBID 8FG
IngestDate Thu Oct 10 17:01:35 EDT 2024
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-proquest_journals_25504799253
OpenAccessLink https://www.proquest.com/docview/2550479925?pq-origsite=%requestingapplication%
PQID 2550479925
PQPubID 2050157
ParticipantIDs proquest_journals_2550479925
PublicationCentury 2000
PublicationDate 20210713
PublicationDateYYYYMMDD 2021-07-13
PublicationDate_xml – month: 07
  year: 2021
  text: 20210713
  day: 13
PublicationDecade 2020
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2021
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 3.3470318
SecondaryResourceType preprint
Snippet In this paper, we propose an Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A. We show how this model can be used to...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Integer programming
Iterative algorithms
Iterative methods
Linear programming
Rhythm
Tiling
Title An Integer Linear Programming Model for Tilings
URI https://www.proquest.com/docview/2550479925
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3NS8MwFH_oiuBtfqFujoBew2iTJstJVFqH4CgyYbfRNFEEnbOdV_9234udHoQdk5APwvvOL-8BXCgltZIjwV2pHZfOaG7T0nIUg6YSyOmxC2iLiRo_yrtZOmsDbk0Lq1zLxCCo3XtFMfIhmr6UDd0k6eXyg1PVKHpdbUtobEMUJ1oTVY_y298YS6I0ThP_xGzQHXkXoqJc-noPtvxiH3YC5LJqDmB4tWAUj3v2NUOPECmOFT9gqTdUJ4yKlL0yNCnZ9IW-jDeHcJ5n05sxX-8yb-mgmf-dWhxBBx16fwwsFqnxzlhbmVI69D-slMhXT9jhNJoIJ9DftNLp5uEe7CaEu6Dkj6IPnVX96c9Qca7sINzOAKLrbFI8YOv-K_sGU3x3rA
link.rule.ids 783,787,12779,21402,33387,33758,43614,43819
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEB60RfTmE6tVA3oNpZtsYk4i0nXVWnpYobdls4kiaG136_93Jm71UOg1IQ_CvPPNDMCVUlIreS24K7Tj0hnNbVxYjmLQlAI5ve8C2mKk0hf5OIknTcCtbmCVS5kYBLX7KilG3kPTl6qhmyi-mc05dY2i39WmhcYmtKVARUOZ4sn9X4wlUhqXiRUxG3RHsgvtcTHz1R5s-Ok-bAXIZVkfQO92yige9-Yrhh4hUhwb_4KlPlGdMGpS9sHQpGTZO6WM14dwmQyyu5QvT8kbOqjz_1uLI2ihQ--PgfVFbLwz1pamkA79Dysl8tUrDjiNJkIHuut2Olk_fQHbafY8zIcPo6dT2IkIg0GFIEUXWovq25-hEl3Y8_BSP3BEd8M
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Integer+Linear+Programming+Model+for+Tilings&rft.jtitle=arXiv.org&rft.au=Auricchio%2C+Gennaro&rft.au=Ferrarini%2C+Luca&rft.au=Lanzarotto%2C+Greta&rft.date=2021-07-13&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422