Séminaire Lotharingien de Combinatoire, 78B.27 (2017), 12 pp.

Jules Depersin, Stéphane Gaubert and Michael Joswig

A Tropical Isoperimetric Inequality

Abstract. We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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