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Article

An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System

1
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2
Department of Mathematics and Computer Sciences, Stetson University, DeLand, FL 32723, USA
3
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
4
Department of Mathematics, Wells College, Aurora, NY 13026, USA
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 311; https://doi.org/10.3390/sym12020311
Received: 8 January 2020 / Revised: 11 February 2020 / Accepted: 12 February 2020 / Published: 21 February 2020
(This article belongs to the Special Issue Symmetry in Numerical Linear and Multilinear Algebra)
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 der Woude. Because our algorithm takes 0 . 088783 sec to solve the eigenvalue problem for Latin square presented in Example 2, while the compared one takes 1 . 718662 sec 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. View Full-Text
Keywords: bipartite min-max-plus systems; eigenvalue and eigenvectors; latin squares bipartite min-max-plus systems; eigenvalue and eigenvectors; latin squares
MDPI and ACS Style

Umer, M.; Hayat, U.; Abbas, F.; Agarwal, A.; Kitanov, P. An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System. Symmetry 2020, 12, 311. https://doi.org/10.3390/sym12020311

AMA Style

Umer M, Hayat U, Abbas F, Agarwal A, Kitanov P. An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System. Symmetry. 2020; 12(2):311. https://doi.org/10.3390/sym12020311

Chicago/Turabian Style

Umer, Mubasher, Umar Hayat, Fazal Abbas, Anurag Agarwal, and Petko Kitanov. 2020. "An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System" Symmetry 12, no. 2: 311. https://doi.org/10.3390/sym12020311

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