dc.contributor.author | Fomin, Fedor | |
dc.contributor.author | Golovach, Petr | |
dc.contributor.author | Inamdar, Tanmay Nitin | |
dc.contributor.author | Zehavi, Meirav | |
dc.date.accessioned | 2023-01-10T11:57:52Z | |
dc.date.available | 2023-01-10T11:57:52Z | |
dc.date.created | 2022-11-04T12:29:36Z | |
dc.date.issued | 2022 | |
dc.identifier.issn | 1868-8969 | |
dc.identifier.uri | https://hdl.handle.net/11250/3042293 | |
dc.description.abstract | The problem of packing of equal disks (or circles) into a rectangle is a fundamental geometric problem. (By a packing here we mean an arrangement of disks in a rectangle without overlapping.) We consider the following algorithmic generalization of the equal disk packing problem. In this problem, for a given packing of equal disks into a rectangle, the question is whether by changing positions of a small number of disks, we can allocate space for packing more disks. More formally, in the repacking problem, for a given set of n equal disks packed into a rectangle and integers k and h, we ask whether it is possible by changing positions of at most h disks to pack n+k disks. Thus the problem of packing equal disks is the special case of our problem with n = h = 0.
While the computational complexity of packing equal disks into a rectangle remains open, we prove that the repacking problem is NP-hard already for h = 0. Our main algorithmic contribution is an algorithm that solves the repacking problem in time (h+k)^𝒪(h+k)⋅|I|^𝒪(1), where |I| is the input size. That is, the problem is fixed-parameter tractable parameterized by k and h. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Schloss Dagstuhl – Leibniz Center for Informatics | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | (Re)packing Equal Disks into Rectangle | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2022 the authors | en_US |
dc.source.articlenumber | 60 | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | https://doi.org/10.4230/LIPIcs.ICALP.2022.60 | |
dc.identifier.cristin | 2069164 | |
dc.source.journal | Leibniz International Proceedings in Informatics | en_US |
dc.source.pagenumber | 60:1-60:17 | en_US |
dc.relation.project | Norges forskningsråd: 314528 | en_US |
dc.identifier.citation | Leibniz International Proceedings in Informatics. 2022, 229, 60:1-60:17. | en_US |
dc.source.volume | 229 | en_US |