8 citations · 28 across the 11 of their papers we have counts for
17 papers
A Quantitative Helly-type Theorem: Containment in a Homothet
Grigory Ivanov, Márton Naszódi
We introduce a new variant of quantitative Helly-type theorems: the minimal \emph{"homothetic distance"} of the intersection of a family of convex sets to the intersection of a sub…
Quantitative Fractional Helly and -Theorems
Attila Jung, Márton Naszódi
We consider quantitative versions of Helly-type questions, that is, instead of finding a point in the intersection, we bound the volume of the intersection. Our first main geometri…
Computing the covering radius of a polytope with an application to lonely runners
Jana Cslovjecsek, Romanos Diogenes Malikiosis, Márton Naszódi +1
We are concerned with the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed f…
Functional John Ellipsoids
Grigory Ivanov, Márton Naszódi
We introduce a new way of representing logarithmically concave functions on . It allows us to extend the notion of the largest volume ellipsoid contained in a conve…
Angular measures and Birkhoff orthogonality in Minkowski planes
Márton Naszódi, Vilmos Prokaj, Konrad Swanepoel
Let and be two unit vectors in a normed plane . We say that is Birkhoff orthogonal to if the line through in the direction supports the unit d…
Approximation of the average of some random matrices
Grigory Ivanov, Márton Naszódi, Alexandr Polyanskii
Rudelson's theorem states that if for a set of unit vectors and positive weights , we have that is the identity operator on …
Colorful Helly-type Theorems for the Volume of Intersections of Convex Bodies
Gábor Damásdi, Viktória Földvári, Márton Naszódi
We prove the following Helly-type result. Let be finite families of convex bodies in . Assume that for any colorful selection o…
Perron and Frobenius meet Carathéodory
Márton Naszódi, Alexandr Polyanskii
We present a new approach of proving certain Carathéodory-type theorems using the Perron-Frobenius Theorem, a classical result in matrix theory describing the largest eigenvalue of…
On the volume bound in the Dvoretzky--Rogers lemma
Ferenc Fodor, Márton Naszódi, Tamás Zarnócz
The classical Dvoretzky--Rogers lemma provides a deterministic algorithm by which, from any set of isotropic vectors in Euclidean -space, one can select a subset of vectors…
Fine approximation of convex bodies by polytopes
Márton Naszódi, Fedor Nazarov, Dmitry Ryabogin
We prove that for every convex body with the center of mass at the origin and every , there exists a convex polytope with at most…
Arrangements of homothets of a convex body
Márton Naszódi, János Pach, Konrad Swanepoel
Answering a question of Füredi and Loeb (1994), we show that the maximum number of pairwise intersecting homothets of a -dimensional centrally symmetric convex body , none of…
Sphere-of-influence graphs in normed spaces
Márton Naszódi, János Pach, Konrad Swanepoel
We show that any -th closed sphere-of-influence graph in a -dimensional normed space has a vertex of degree less than~, thus obtaining a common generalization of resul…
Flavors of Translative Coverings
Márton Naszódi
We survey results on the problem of covering the space , or a convex body in it, by translates of a convex body. Our main goal is to present a diverse set of methods…
A Spiky Ball
Márton Naszódi
The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean -space by a minimum number of translates of its interior. By a probabilistic argume…
On some covering problems in geometry
Márton Naszódi
We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean -s…
On multiple Borsuk numbers in normed spaces
Zsolt Lángi, Márton Naszódi
Hujter and Lángi introduced the -fold Borsuk number of a set in Euclidean -space of diameter as the smallest cardinality of a family of subsets of $S…
Push forward measures and concentration phenomena
C. Hugo JimÉnez, MÁrton NaszÓdi, Rafael Villa
In this note we study how a concentration phenomenon can be transmitted from one measure to a push-forward measure . In the first part, we push forward by $π:supp(μ)\rig…