An algorithm for solving an overdetermined tropical linear system with the help of analysis of stable solutions of subsystems

In this paper we show that an overdetermined tropical linear system has a solution if and only if it contains a square subsystem with a stable solution which is a solution of the initial system. This leads us to a simple algorithm solving tropical linear systems in $O(C_m^nn^4)$ time, where $m$ is a number of equations and $n$ is a number of variables. In the particular case of weekly overdetermined systems this time is polynomial.