Browsing by Author "Martínez Moraian, Alejandra"

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    • A connection between Inverse Problems and Nonstandard Analysis 

      Martínez Moraian, Alejandra (Universitat Politècnica de Catalunya, 2018-10)
      Master thesis
      Restricted access - author's decision
      Nonstandard analysis was born in the decade of 1960 an attempt to give a formal context to the Leibniz approach to differential calculus, in particular in order to provide a rigorous foundation to the notions of infinitesimal ...

    • On circles enclosing many points 

      Claverol Aguas, Mercè; Huemer, Clemens; Martínez Moraian, Alejandra (2021-10-01)
      Article
      Open Access
      We prove that every set of n red and n blue points in the plane contains a red and a blue point such that every circle through them encloses at least points of the set. This is a two-colored version of a problem posed by ...

    • Optimizing generalized kernels of polygons 

      Martínez Moraian, Alejandra; Orden Martin, David; Palios, Leonidas; Seara Ojea, Carlos; Zylinski, Pawel (Springer Nature, 2021-04-09)
      Article
      Open Access
      Let O be a set of k orientations in the plane, and let P be a simple polygon in the plane. Given two points p, q inside P, we say that p O-sees q if there is an O-staircase contained in P that connects p and q. The O-Kernel ...

    • The edge labeling of higher order Voronoi diagrams 

      Claverol Aguas, Mercè; de las Heras Parrilla, Andrea; Huemer, Clemens; Martínez Moraian, Alejandra (2021)
      Conference report
      Open Access
      We present an edge labeling of order-k Voronoi diagrams, Vk(S), of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that Vk(S) has a small orientable cycle and path double ...