Andrei Comăneci
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View article: Breakdown points of Fermat–Weber problems under gauge distances
Breakdown points of Fermat–Weber problems under gauge distances Open
We compute the robustness of Fermat–Weber points with respect to any finite gauge. We show a breakdown point of $$1/(1+\sigma )$$ where $$\sigma $$ is the asymmetry measure of the gauge. We obtain quantitative results indicating…
View article: Asymmetric tropical distances and power diagrams
Asymmetric tropical distances and power diagrams Open
We investigate Voronoi diagrams with respect to an asymmetric tropical distance function, in particular for infinite point sets. These Voronoi diagrams turn out to be much better behaved than those arising from the standard tropical distan…
View article: Tropical convexity in location problems
Tropical convexity in location problems Open
We investigate location problems whose optimum lies in the tropical convex hull of the input points. Firstly, we study geodesically star-convex sets under the asymmetric tropical distance and introduce the class of tropically quasiconvex f…
View article: Tropical medians by transportation
Tropical medians by transportation Open
Fermat–Weber points with respect to an asymmetric tropical distance function are studied. It turns out that they correspond to the optimal solutions of a transportation problem. The results are applied to obtain a new method for computing …
View article: Breakdown points of Fermat-Weber problems under gauge distances
Breakdown points of Fermat-Weber problems under gauge distances Open
We compute the robustness of Fermat-Weber points with respect to any finite gauge. We show a breakdown point of $1/(1+σ)$ where $σ$ is the asymmetry measure of the gauge. We obtain quantitative results indicating how far a corrupted Fermat…
View article: Parametric Fermat-Weber and tropical supertrees
Parametric Fermat-Weber and tropical supertrees Open
We study a parametric version of the Fermat-Weber problem with respect to an asymmetric distance function, which occurs naturally in tropical geometry. Our results yield a method for constructing phylogenetic supertrees.
View article: Asymmetric tropical distances and power diagrams
Asymmetric tropical distances and power diagrams Open
We investigate the Voronoi diagrams with respect to an asymmetric tropical distance function, also for infinite point sets. These turn out to be much better behaved than the tropical Voronoi diagrams arising from the standard tropical dist…
View article: Tropical medians by transportation
Tropical medians by transportation Open
Fermat-Weber points with respect to an asymmetric tropical distance function are studied. It turns out that they correspond to the optimal solutions of a transportation problem. The results are applied to obtain a new method for computing …
View article: On Fryszkowski’s problem
On Fryszkowski’s problem Open
In this paper we give two partial answers to Fryszkowski's problem which can be stated as follows: given $\alpha \in (0,1)$, an arbitrary non-empty set $\Omega$ and a set-valued mapping $F:\Omega \rightarrow 2^{\Omega }$, find necessary an…