3 citations · 11 across the 13 of their papers we have counts for
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Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
Romanos Diogenes Malikiosis, Francisco Santos, Matthias Schymura
Tao (2018) showed that in order to prove the Lonely Runner Conjecture (LRC) up to runners it suffices to consider positive integer velocities in the order of . Us…
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…
Complexity of linear relaxations in integer programming
Gennadiy Averkov, Matthias Schymura
For a set of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with is called the relaxation complexity…
The covering radius and a discrete surface area for non-hollow simplices
Giulia Codenotti, Francisco Santos, Matthias Schymura
We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of in dimension , achieved by the "stand…
A note on discrete lattice-periodic sets with an application to Archimedean tilings
Matthias Schymura, Liping Yuan
Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that every Archimedean tiling is the union of…
Lonely Runner Polyhedra
Matthias Beck, Serkan Hosten, Matthias Schymura
We study the \emph{Lonely Runner Conjecture}, conceived by Jörg M.~Wills in the 1960's: Given positive integers , there exists a positive real number such…