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Person# Márton Naszódi

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Radoslav Fulek, Márton Naszódi, Sebastian Urban Stich

Let P be a finite point set in the plane. A \emph{c-ordinary triangle} in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question of Erd\H{o}s, and answering a question of de Zeeuw, we prove that there exists a constant c>0 such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(|P|).

We showthat any k-th closed sphere-of-influence graph in a d-dimensional normed space has a vertex of degree less than 5dk, thus obtaining a common generalization of results of Furedi and Loeb (Proc AmMath Soc 121(4): 1063-1073, 1994 [1]) and Guibas et al. (Sphere-of-influence graphs in higher dimensions, Intuitive geometry [Szeged, 1991], 1994, pp. 131-137 [2]).

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We present faster algorithms for the approximate Closest Vector Problem under l_p norms

2019