2016/12/06 by Georg Loho, Loho, Georg · 1 citation
Mathematics · #05E45 #14T05 #52C40 #90C05 #91A50 #Combinatorics (math.CO) #FOS: Mathematics #Optimization and Control (math.OC) #math.CO #math.OC #msc:05E45 #msc:14T05 #msc:52C40 #msc:90C05 #msc:91A50
paper · pdf · doi:10.48550/arxiv.1612.01890
56 pages, 25 figures; essential improvements in results and exposition
arxiv created 2017/12/04 · arxiv updated 2017/12/05
In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the product of two simplices and the combinatorics of the associated set of bipartite graphs with an additional sign information which we call a signed tropical matroid. We demonstrate the connections with the classical simplex method, mean payoff games and scheduling.