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dc.contributor.authorAbbott, Timothy G.
dc.contributor.authorBurr, Michael A.
dc.contributor.authorChan, Timothy M.
dc.contributor.authorDemaine, Erik D.
dc.contributor.authorDemaine, Martin L.
dc.contributor.authorHugg, John
dc.contributor.authorKane, Daniel
dc.contributor.authorLangerman, Stefan
dc.contributor.authorNelson, Jelani
dc.contributor.authorRafalin, Eynat
dc.contributor.authorSeyboth, Kathryn
dc.contributor.authorYeung, Vincent
dc.date.accessioned2015-03-25T18:34:46Z
dc.date.available2015-03-25T18:34:46Z
dc.date.issued2009-01
dc.date.submitted2008-02
dc.identifier.issn09257721
dc.identifier.urihttp://hdl.handle.net/1721.1/96191
dc.description.abstractWe design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n[1 over 3]+ε) amortized time and O(n[4 over 3]+ε) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O(logn) time and ham-sandwich queries in O(klog4n)O(klog4n) time. In addition, if each point set has convex peeling depth k, then we can maintain the decomposition automatically using O(klogn) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O(klog[superscript 4]n) time plus the O((kb)polylog(kb)) time required to approximate the root of a polynomial of degree O(k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.en_US
dc.language.isoen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.comgeo.2008.09.008en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceElsevieren_US
dc.titleDynamic ham-sandwich cuts in the planeen_US
dc.typeArticleen_US
dc.identifier.citationAbbott, Timothy G., Michael A. Burr, Timothy M. Chan, Erik D. Demaine, Martin L. Demaine, John Hugg, Daniel Kane, et al. “Dynamic Ham-Sandwich Cuts in the Plane.” Computational Geometry 42, no. 5 (July 2009): 419–428. © 2009 Elsevier B.V.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.mitauthorDemaine, Erik D.en_US
dc.contributor.mitauthorAbbott, Timothy G.en_US
dc.contributor.mitauthorDemaine, Martin L.en_US
dc.contributor.mitauthorYeung, Vincenten_US
dc.contributor.mitauthorNelson, Jelanien_US
dc.relation.journalComputational Geometryen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsAbbott, Timothy G.; Burr, Michael A.; Chan, Timothy M.; Demaine, Erik D.; Demaine, Martin L.; Hugg, John; Kane, Daniel; Langerman, Stefan; Nelson, Jelani; Rafalin, Eynat; Seyboth, Kathryn; Yeung, Vincenten_US
dc.identifier.orcidhttps://orcid.org/0000-0003-3803-5703
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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