M. Dobbins

activity

20152026

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Showing 2018Show all

2 papers · 1 filter

cs.CG2018

Smoothed Analysis of the Art Gallery Problem

Michael Gene Dobbins, Andreas Holmsen, Tillmann Miltzow

In the Art Gallery Problem we are given a polygon $P \subset [0, L]^{2}$ on $n$ vertices and a number $k$ . We want to find a guard set $G$ of size $k$ , such that each point in $P$ is s…

math.MG2018

Barycenters of points in polytope skeleta

Michael Gene Dobbins, Florian Frick

The first author showed that for a given point $p$ in an $nk$ -polytope $P$ there are $n$ points in the $k$ -faces of $P$ , whose barycenter is $p$ . We show that we can increase the d…