Show simple item record

dc.contributor.authorBremner, David
dc.contributor.authorChan, Timothy M.
dc.contributor.authorDemaine, Erik D
dc.contributor.authorErickson, Jeff
dc.contributor.authorHurtado, Ferran
dc.contributor.authorIacono, John
dc.contributor.authorLangerman, Stefan
dc.contributor.authorTaslakian, Perouz
dc.date.accessioned2019-06-21T16:40:12Z
dc.date.available2019-06-21T16:40:12Z
dc.date.issued2012-12
dc.date.submitted2012-12
dc.identifier.issn0178-4617
dc.identifier.issn1432-0541
dc.identifier.urihttps://hdl.handle.net/1721.1/121377
dc.description.abstractWe give subquadratic algorithms that, given two necklaces each with n beads at arbitrary positions, compute the optimal rotation of the necklaces to best align the beads. Here alignment is measured according to the lp norm of the vector of distances between pairs of beads from opposite necklaces in the best perfect matching. We show surprisingly different results for p = 1, p even, and p =∞ .For p even, we reduce the problem to standard convolution, while for p =∞ and p = 1, we reduce the problem to ( min , + ) convolution and ( median , + ) convolution. Then we solve the latter two convolution problems in subquadratic time, which are interesting results in their own right. These results shed some light on the classic sorting X + Y problem, because the convolutions can be viewed as computing order statistics on the antidiagonals of the X + Y matrix. All of our algorithms run in o(n²) time, whereas the obvious algorithms for these problems run in Θ(n 2 ) time.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grant CCF-0430849)en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (grant OISE-0334653)en_US
dc.description.sponsorshipAlfred P. Sloan Fellowshipen_US
dc.language.isoen
dc.publisherSpringer Nature America, Incen_US
dc.relation.isversionof10.1007/S00453-012-9734-3en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleNecklaces, Convolutions, and X+Yen_US
dc.typeArticleen_US
dc.identifier.citationBremner, David, Timothy M. Chan, Erik D. Demaine, Jeff Erickson, Ferran Hurtado, John Iacono, Stefan Langerman and Perouz Taslakian. "Necklaces, Convolutions, and X + Y." Algorithmica, Vol. 69 (2) June 2014: 294-314.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.relation.journalAlgorithmicaen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2019-06-18T19:13:23Z
dspace.date.submission2019-06-18T19:13:24Z
mit.journal.volume69en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record