An Algorithm for Solving an Overdetermined Tropical Linear System Using the Analysis of Stable Solutions of Subsystems
Journal of Mathematical Sciences(2018)
摘要
In this paper, we show that an overdetermined tropical linear system has a solution if and only if it contains a square subsystem having a stable solution that is a solution of the original system. This leads to a simple algorithm for solving tropical linear systems in time O((_n^m))n^4 , where m is the number of equations and n is the number of variables. For weakly overdetermined systems, this time is polynomial.
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