Conditions for the structural existence of an eigenvalue of a bipartite (min, max, +)-system

Jacob Van der Woude*, Subiono

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

18 Citations (Scopus)

Abstract

In this paper we consider bipartite (min, max, +)-systems. We present conditions for the structural existence of an eigenvalue and corresponding eigenvector for such systems, where both the eigenvalue and eigenvector are supposed to be finite. The conditions are stated in terms of the system matrices that describe a bipartite (min, max, +)-system. Structural in the previous means that not so much the numerical values of the finite entries in the system matrices are important, rather than their locations within these matrices. The conditions presented in this paper can be seen as an extension towards bipartite (min, max, +)-systems of known conditions for the structural existence of an eigenvalue of a (max, +)-system involving the (ir)reducibility of the associated system matrix. Although developed for bipartite (min, max, +)-systems, the conditions for the structural existence of an eigenvalue also can directly be applied to general (min, max, +)-systems when given in the so-called conjunctive or disjunctive normal form.

Original languageEnglish
Pages (from-to)13-24
Number of pages12
JournalTheoretical Computer Science
Volume293
Issue number1
DOIs
Publication statusPublished - 3 Feb 2003
EventMax-Plus Algebras - Vendee, France
Duration: 4 May 19987 May 1998

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