Tropical medians by transportation

In this talk, we present the Fermat–Weber problem under an asymmetric tropical distance. We describe the location of the optimum in terms of tropical geometry, which gives a combinatorial interpretation of the set of solutions. Moreover, it turns out that this location problem is equivalent to a transportation problem, allowing for fast computation. Finally, we show how we can exploit the connection to tropical convexity for an application to the consensus problem from computational biology. The geometric interpretation also gives desirable properties for the resulting consensus method.