Max-Plus Linear Algebra and Its Applications

Abstract

Abstract. The max-plus algebra is a semiring with addition “max” and multiplication “+”. The study of the max-plus algebra originated from manufacturing and has been developed independently in various elds of theory and application. In the present paper, we focus on the eigenvalue problem over the max-plus algebra and explain the fundamental facts including computational algorithms. We also introduce recent theoretical developments in the eigenvalue problem. Further, we describe applications of the eigenvalue problem to discrete event systems and integrable systems.