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Generalized public transportation scheduling using max-plus algebra

“…The max-plus spectral problem is a problem of determining the max-plus eigenvalue and corresponding maxplus eigenvectors of a given square matrix A ∈ R n×n ε [2,15]. This problem is related to the explicit first-order autonomous MPL systems (3) and can be solved by using the power algorithm [21]. Definition 2.2.…”

“…The power algorithm developed in [21] can be used to determine the max-plus eigenvalue and a corresponding max-plus eigenvector of matrix A ∈ R n×n ε . The algorithm leverages recurrence relation x(k + 1) = A ⊗ x(k) and uses finite initial condition…”

“…To the best of our knowledge, by using the standard approach [2,15], we cannot design such systematic procedure. Finally, in the third step, we determine the regular schedule by using the power algorithm [21]. In each step, we provide detailed explanations in order to convince the reader that those steps are systematic.…”

An Efficient Algorithm for Nontrivial Eigenvectors in Max-Plus Algebra

“…Eigenproblems are the problems of finding an eigenvalue λ and an eigenvector v from an n × n matrix M such that Mv = λv. The algorithm in [9] can solve these problems.…”

“…A novel iterative method is proposed for the computation of eigenvalue and the corresponding eigenvectors in max-plus algebra. To evaluate the eigenvalue and the corresponding eigenvectors of discrete event systems, some algorithms have been established in [8][9][10][11]. The first algorithm to determine the eigenvalue was given by Karp [12].…”