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DESCRIPTION: Several new results about the largest possible diameter of a l
attice polytope contained in the hypercube [0\,k]^d\, a quantity related to
the complexity of the simplex algorithm\, will be presented. Upper bounds
on this quantity have been known for a couple of decades and have been impr
oved recently. In this lecture\, conjecturally sharp lower bounds on this q
uantity will be presented for all d and k\, as well as exact asymptotic est
imates when d is fixed and k grows large. These lower bounds are obtained b
y computing the largest diameter a lattice zonotope contained in the hyperc
ube [0\,k]^d can have\, answering a question by Günter Rote. This talk is b
ased on joint work with Antoine Deza and Noriyoshi Sukegawa.
DTSTAMP:20200122T133500
DTSTART:20200210T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Lionel Pournin (Université Paris 13): Recent results on the diamete
r of lattice polytopes
UID:95692732@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20200210-L-Pournin.html
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