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dc.contributor.authorAhn, Heekap
dc.contributor.authorBae, Sangwon
dc.contributor.authorCheong, Otfried
dc.contributor.authorGudmundsson, Joachim
dc.contributor.authorTokuyama, Takeshi
dc.contributor.authorVigneron, Antoine E.
dc.date.accessioned2015-08-24T09:25:19Z
dc.date.available2015-08-24T09:25:19Z
dc.date.issued2012
dc.identifier.citationAhn HK., Bae S.W., Cheong O., Gudmundsson J., Tokuyama T., Vigneron A. (2012) A Generalization of the Convex Kakeya Problem. In: Fernández-Baca D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg
dc.identifier.isbn9783642293436
dc.identifier.issn03029743
dc.identifier.doi10.1007/978-3-642-29344-3_1
dc.identifier.urihttp://hdl.handle.net/10754/575754
dc.description.abstractWe consider the following geometric alignment problem: Given a set of line segments in the plane, find a convex region of smallest area that contains a translate of each input segment. This can be seen as a generalization of Kakeya's problem of finding a convex region of smallest area such that a needle can be turned through 360 degrees within this region. Our main result is an optimal Θ(n log n)-time algorithm for our geometric alignment problem, when the input is a set of n line segments. We also show that, if the goal is to minimize the perimeter of the region instead of its area, then the optimum placement is when the midpoints of the segments coincide. Finally, we show that for any compact convex figure G, the smallest enclosing disk of G is a smallest-perimeter region containing a translate of any rotated copy of G. © 2012 Springer-Verlag Berlin Heidelberg.
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/chapter/10.1007%2F978-3-642-29344-3_1
dc.titleA generalization of the convex Kakeya problem
dc.typeConference Paper
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentGeometric Algorithms Group
dc.identifier.journalLATIN 2012: Theoretical Informatics
dc.conference.date16 April 2012 through 20 April 2012
dc.conference.name10th Latin American Symposiumon Theoretical Informatics, LATIN 2012
dc.conference.locationArequipa
dc.contributor.institutionPOSTECH, South Korea
dc.contributor.institutionKyonggi University, South Korea
dc.contributor.institutionKAIST, South Korea
dc.contributor.institutionUniversity of Sydney, Australia
dc.contributor.institutionTohoku University, Japan
dc.identifier.arxivid1209.2171
kaust.personVigneron, Antoine E.


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