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DESCRIPTION: The Fermat-Weber problem seeks a point that minimizes the aver
age distance from a given sample. The problem was studied by Lin and Yoshid
a (2018) using the standard tropical metric with the purpose of analyzing p
hylogenetic data. In this talk\, we argue that using a related asymmetric d
istance we have better geometric and algorithmic properties. The new formul
ation is strongly related to tropical convexity and is equivalent to a tran
sportation problem. This gives a geometric perspective to the transportatio
n problem\, which was exploited by Tokuyama and Nakano (1995) to obtain eff
icient 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.
DTSTAMP:20220609T205500
DTSTART:20220613T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Andrei Comăneci (Technische Universität Berlin): Tropical Medians b
y Transportation
UID:107920444@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220613-C-Comaneci.html
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