TY - JOUR
T1 - Conditions for the structural existence of an eigenvalue of a bipartite (min, max, +)-system
AU - Van der Woude, Jacob
AU - Subiono,
PY - 2003/2/3
Y1 - 2003/2/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0037415366&partnerID=8YFLogxK
U2 - 10.1016/S0304-3975(02)00229-3
DO - 10.1016/S0304-3975(02)00229-3
M3 - Conference article
AN - SCOPUS:0037415366
SN - 0304-3975
VL - 293
SP - 13
EP - 24
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 1
T2 - Max-Plus Algebras
Y2 - 4 May 1998 through 7 May 1998
ER -