15 citations · 23 across the 5 of their papers we have counts for
5 papers
Tropical convexity in location problems
Andrei Comăneci
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 d…
Breakdown points of Fermat-Weber problems under gauge distances
Andrei Comăneci, Frank Plastria
We compute the robustness of Fermat-Weber points with respect to any finite gauge. We show a breakdown point of where is the asymmetry measure of the gauge. We obtain…
Parametric Fermat-Weber and tropical supertrees
Andrei Comăneci, Michael Joswig
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 f…
Asymmetric tropical distances and power diagrams
Andrei Comăneci, Michael Joswig
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 tropic…
Tropical medians by transportation
Andrei Comăneci, Michael Joswig
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. Th…