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dc.contributor.authorBalogh, János
dc.contributor.authorDósa, György
dc.contributor.authorHvattum, Lars Magnus
dc.contributor.authorOlaj, Tomas
dc.contributor.authorTuza, Zsolt
dc.date.accessioned2024-03-13T11:53:32Z
dc.date.available2024-03-13T11:53:32Z
dc.date.created2022-04-10T15:56:09Z
dc.date.issued2022
dc.identifier.citationOptimization Letters. 2022, 16 (9), 2775-2785.en_US
dc.identifier.issn1862-4472
dc.identifier.urihttps://hdl.handle.net/11250/3122119
dc.description.abstractMore than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes 1, 2,..., n can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than N :=√n(n + 1)(2n + 1)/6) is not possible. Here we prove that an asymptotically minimal packing exists in a square of size N +cn+O(√n) with c < 1, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Keywords: Square packing · Guillotine cut · Asymptotic analysis · Gardner’s problem · Square the square · Recursive algorithm.en_US
dc.language.isoengen_US
dc.relation.urihttps://doi.org/10.1007/s11590-022-01858-w
dc.rightsNavngivelse 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.no*
dc.titleGuillotine cutting is asymptotically optimal for packing consecutive squaresen_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.description.versionpublishedVersionen_US
dc.source.pagenumber2775-2785en_US
dc.source.volume16en_US
dc.source.journalOptimization Lettersen_US
dc.source.issue9en_US
dc.identifier.doi10.1007/s11590-022-01858-w
dc.identifier.cristin2016517
cristin.ispublishedtrue
cristin.fulltextoriginal
cristin.qualitycode1


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Navngivelse 4.0 Internasjonal
Except where otherwise noted, this item's license is described as Navngivelse 4.0 Internasjonal