An efficient algorithm for critical circuits and finite eigenvectors in the max-plus algebra Original Research Article

We consider the eigenvalue problem in the max-plus algebra for matrices in image but with eigenvectors in image . The problem is relaxed to a linear optimization (LO) problem of which the dual problem is solved by finding a maximal average weight circuit in the graph of the matrix. The Floyd–Warshall procedure is used to find such a circuit. This procedure also provides an efficient algorithm for finding an eigenvector.