An efficient algorithm for eigenvalue problem of latin squares in a bipartite min-max-plus system

Abstract

In this paper, we consider the eigenproblems for Latin squares in a bipartite min-max-plus system. The focus is upon developing a new algorithm to compute the eigenvalue and eigenvectors (trivial and non-trivial) for Latin squares in a bipartite min-max-plus system. We illustrate the algorithm using some examples. The proposed algorithm is implemented in MATLAB, using max-plus algebra toolbox. Computationally speaking, our algorithm has a clear advantage over the power algorithm presented by Subiono and van derWoude. Because our algorithm takes 0.088783 s to solve the eigenvalue problem for Latin square presented in Example 2, while the compared one takes 1.718662 s for the same problem. Furthermore, a time complexity comparison is presented, which reveals that the proposed algorithm is less time consuming when compared with some of the existing algorithms.