Abstract
This work discusses the eigenproblems of bipartite (min, max, +)-systems when the system matrices are Latin squares. We propose an approach to characterize and compute the eigenvalue, trivial eigenvectors and nontrivial eigenvectors. The time complexity of the overall approach is a polynomial w.r.t. the dimension of the system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baccelli F, Cohen G, Olsder G, Quadrat JP (1992) Synchronization and linearity, an algebra for discrete event systems. Wiley, New York
Gaubert S, Gunawardena J (2004) The Perron-Frobenius theorem for homogeneous, monotone functions. Trans Am Math Soc 356(12):4931–4950
Gavalec M, Plavka J (2008) Structure of the eigenspace of a Monge matrix in max-plus algebra. Discret Appl Math 156(5):596–606
Gunawardena J (1994) Min-max functions. Discret Event Dyn Sys 4(4):377–407
Heidergott B, Olsder G, van der Woude J (2006) Max plus at work–modeling and analysis of synchronized systems: A course on max-plus algebra and its applications. Princeton University Press, Princeton
Hulpke A, Kaski P, Östergård P (2011) The number of latin squares of order 11. Math Comput 80(274):1197–1219
Imaev A, Judd R (2010) Computing an eigenvector of an inverse Monge matrix in maxplus algebra. Discret Appl Math 158(15):1701–1707
McKay B, Wanless I (2005) On the number of latin squares. Ann Comb 9(3):335–344
Mufid MS, Subiono (2014) Eigenvalues and eigenvectors of latin squares in max-plus algebra. J Indones Math Soc 20(1):37–45
Olsder G (1991) Eigenvalues of dynamic max-min systems. Discret Event Dyn Syst 1(2):177–207
Rotmann J (2003) Advance modern algebra. Prentice Hall, New Jersey
Stones D (2010) On the number of latin rectangles. Ph.D. thesis, Monash University
Subiono (2000) On classes of min-max-plus systems and their applications. Ph.D. thesis, Delft University of Technology
Subiono, van der Woude J (2000) Power algorithms for (max, +)- and bipartite (min, max, +)-systems. Discret Event Dyn Syst 10(4):369–389
Tomášková H (2010) Eigenproblem for circulant matrices in max-plus algebra. In: Proceedings of the 12th WSEAS international conference on mathematical methods, computational techniques and intelligent systems (MAMECTIS’10), pp 158–161
van der Woude J, Subiono (2003) Conditions for the structural existence of an eigenvalue of a bipartite (min, max, +)-system. Theor Comput Sci 293(1):13–24
Author information
Authors and Affiliations
Corresponding author
Additional information
The second author is grateful to LPDP (Lembaga Pengelola Dana Pendidikan) from Ministry of Finance for partially supporting this research.
Rights and permissions
About this article
Cite this article
Subiono, ᅟ., Mufid, M.S. & Adzkiya, D. Eigenproblems of latin squares in bipartite (min,max,+)-systems. Discrete Event Dyn Syst 26, 657–668 (2016). https://doi.org/10.1007/s10626-014-0204-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10626-014-0204-8