On Farey table and its compression for space optimization with guaranteed error bounds

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dc.contributor.authorParia, B.
dc.contributor.authorPratihar, S.
dc.contributor.authorBhowmick, P.
dc.coverage.issue2cs
dc.coverage.volume5cs
dc.date.accessioned2017-02-03T11:15:55Z
dc.date.available2017-02-03T11:15:55Z
dc.date.issued2016cs
dc.description.abstractFarey sequences, introduced by such renowned mathematicians as John Farey, Charles Haros, and Augustin-L. Cauchy over 200 years ago, are quite well- known by today in theory of fractions, but its computational perspectives are pos- sibly not yet explored up to its merit. In this paper, we present some novel theoret- ical results and e cient algorithms for representation of a Farey sequence through a Farey table. The ranks of the fractions in a Farey sequence are stored in the Farey table to provide an e cient solution to the rank problem, thereby aiding in and speeding up any application frequently requiring fraction ranks for computational speed-up. As the size of the Farey sequence grows quadratically with its order, the Farey table becomes inadvertently large, which calls for its (lossy) compression up to a permissible error. We have, therefore, proposed two compression schemes to obtain a compressed Farey table (CFT). The necessary analysis has been done in detail to derive the error bound in a CFT. As the nal step towards space opti- mization, we have also shown how a CFT can be stored in a 1-dimensional array. Experimental results have been furnished to demonstrate the characteristics and e ciency of a Farey table and its compressed form.en
dc.formattextcs
dc.format.extent123-145cs
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMathematics for Applications. 2016 vol. 5, č. 2, s. 123-145. ISSN 1805-3629cs
dc.identifier.doi10.13164/ma.2016.09en
dc.identifier.issn1805-3629
dc.identifier.urihttp://hdl.handle.net/11012/63785
dc.language.isoencs
dc.publisherVysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.relation.ispartofMathematics for Applicationsen
dc.relation.urihttp://ma.fme.vutbr.cz/archiv/5_2/ma_5_2_paria_et_al_final.pdfcs
dc.rights© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.rights.accessopenAccessen
dc.subjectFarey sequenceen
dc.subjectFarey tableen
dc.subjectfraction ranken
dc.subjectfraction erroren
dc.subjectrank problemen
dc.subjectdigital ge- ometryen
dc.subjectdigital image processingen
dc.titleOn Farey table and its compression for space optimization with guaranteed error boundsen
dc.type.driverotheren
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
eprints.affiliatedInstitution.departmentÚstav matematikycs
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
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