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dc.contributor.authorBuchin, Kevin
dc.contributor.authorBuchin, Maike
dc.contributor.authorKreveld, Marc van
dc.contributor.authorLöffler, Maarten
dc.contributor.authorSilveira, Rodrigo Ignacio
dc.contributor.authorWenk, Carola
dc.contributor.authorWiratma, Lionov
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.date.accessioned2013-02-14T14:40:06Z
dc.date.available2013-02-14T14:40:06Z
dc.date.created2012-05
dc.date.issued2012-05
dc.identifier.citationBuchin, K. [et al.]. Median trajectories. "Algorithmica", Maig 2012, p. 1-20.
dc.identifier.issn0178-4617
dc.identifier.urihttp://hdl.handle.net/2117/17768
dc.description.abstractWe investigate the concept of a median among a set of trajectories. We establish criteria that a “median trajectory” should meet, and present two different methods to construct a median for a set of input trajectories. The first method is very simple, while the second method is more complicated and uses homotopy with respect to sufficiently large faces in the arrangement formed by the trajectories. We give algorithms for both methods, analyze the worst-case running time, and show that under certain assumptions both methods can be implemented efficiently. We empirically compare the output of both methods on randomly generated trajectories, and evaluate whether the two methods yield medians that are according to our intuition. Our results suggest that the second method, using homotopy, performs considerably better.
dc.format.extent20 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
dc.subject.lcshTrajectories
dc.subject.lcshGeometric algorithms
dc.subject.lcshHomotopy
dc.titleMedian trajectories
dc.typeArticle
dc.subject.lemacGeometria computacional
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.identifier.doi10.1007/s10707-011-0143-6
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://cataleg.upc.edu/record=b1018082~S1*cat
dc.rights.accessOpen Access
local.identifier.drac11026777
dc.description.versionPostprint (author’s final draft)
local.citation.authorBuchin, K.; Buchin, M.; Kreveld, M. van; Löffler, M.; Silveira, R.I.; Wenk, C.; Wiratma, L.
local.citation.publicationNameAlgorithmica
local.citation.startingPage1
local.citation.endingPage20


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