English

Abstract tropical linear programming

Optimization and Control 2017-12-05 v2 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1612.01890,
  title  = {Abstract tropical linear programming},
  author = {Georg Loho},
  journal= {arXiv preprint arXiv:1612.01890},
  year   = {2017}
}

Comments

56 pages, 25 figures; essential improvements in results and exposition