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Colloquium by Andrei Comăneci (Technische Universität Berlin): Tropical Medians by Transportation

Jun 13, 2022 | 04:00 PM s.t.

The Fermat-Weber problem seeks a point that minimizes the average distance from a given sample. The problem was studied by Lin and Yoshida (2018) using the standard tropical metric with the purpose of analyzing phylogenetic data. In this talk, we argue that using a related asymmetric distance we have better geometric and algorithmic properties. The new formulation is strongly related to tropical convexity and is equivalent to a transportation problem. This gives a geometric perspective to the transportation problem, which was exploited by Tokuyama and Nakano (1995) to obtain efficient algorithms. At the end, we will see an application to computational biology: a new method for computing consensus trees. The talk is based on joint work with Michael Joswig.

Time & Location

Jun 13, 2022 | 04:00 PM s.t.

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
Room MA 041 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)