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dc.contributor.authorGray, Chris
dc.contributor.authorKammer, Frank
dc.contributor.authorLöffler, Maarten
dc.contributor.authorSilveira, Rodrigo Ignacio
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.identifier.citationGray, C. [et al.]. Removing local extrema from imprecise terrains. "Computational geometry: theory and applications", Agost 2012, vol. 45, núm. 7, p. 334-349.
dc.description.abstractIn this paper we consider imprecise terrains, that is, triangulated terrains with a vertical error interval in the vertices. In particular, we study the problem of removing as many local extrema (minima and maxima) as possible from the terrain; that is, fi nding an assignment of one height to each vertex, within its error interval, so that the resulting terrain has minimum number of local extrema. We show that removing only minima or only maxima can be done optimally in O(n log n) time, for a terrain with n vertices. Interestingly, however, the problem of fi nding a height assignment that minimizes the total number of local extrema (minima as well as maxima) is NP-hard, and is even hard to approximate within a factor of O(log log n) unless P = NP. Moreover, we show that even a simpli ed version of the problem where we can have only three di fferent types of intervals for the vertices is already NP-hard, a result we obtain by proving hardness of a special case of 2-Disjoint Connected Subgraphs, a problem that has lately received considerable attention from the graph-algorithms community.
dc.format.extent16 p.
dc.subjectÀrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
dc.subject.lcshData imprecision
dc.subject.lcshDigital elevation models
dc.subject.otherData imprecision
dc.subject.otherLocal minima
dc.subject.otherTerrain analysis
dc.titleRemoving local extrema from imprecise terrains
dc.subject.lemacModels geomètrics -- Disseny assistit per ordinador
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
upcommons.citation.authorGray, C.; Kammer, F.; Löffler, M.; Silveira, R.I.
upcommons.citation.publicationNameComputational geometry: theory and applications

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