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The primary objectives of Graphs, Dioïds and Semirings: New Models and Algorithms are to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties, while demonstrating the modeling and problem-solving capability and flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by nonclassical algebraic structures, which either extend usual algebra (i.e., semirings), or correspond to a new branch of algebra (i.e., dioïds), apart from the classical structures of groups, rings, and fields.…mehr

Produktbeschreibung
The primary objectives of Graphs, Dioïds and Semirings: New Models and Algorithms are to emphasize the deep relations existing between the semiring and dioïd structures with graphs and their combinatorial properties, while demonstrating the modeling and problem-solving capability and flexibility of these structures. In addition the book provides an extensive overview of the mathematical properties employed by nonclassical algebraic structures, which either extend usual algebra (i.e., semirings), or correspond to a new branch of algebra (i.e., dioïds), apart from the classical structures of groups, rings, and fields.
  • Produktdetails
  • Operations Research/Computer Science Interfaces Series 41
  • Verlag: Springer / Springer US / Springer, Berlin
  • Artikelnr. des Verlages: 11395485
  • Erscheinungstermin: Juni 2008
  • Englisch
  • Abmessung: 241mm x 160mm x 26mm
  • Gewicht: 704g
  • ISBN-13: 9780387754499
  • ISBN-10: 0387754490
  • Artikelnr.: 23117293
Autorenporträt
Michel Gondran, Université Pierre et Marie Curie - CNRS, France / Michel Minoux, Université Pierre et Marie Curie - CNRS, France
Inhaltsangabe
Pre-Semirings, Semirings and Dioids.- Combinatorial Properties of (Pre)-Semirings.- Topology on Ordered Sets: Topological Dioids.- Solving Linear Systems in Dioids.- Linear Dependence and Independence in Semi-Modules and Moduloids.- Eigenvalues and Eigenvectors of Endomorphisms.- Dioids and Nonlinear Analysis.- Collected Examples of Monoids, (Pre)-Semirings and Dioids.
Rezensionen
From the reviews: "The authors carefully explain with examples what is meant by a canonically ordered monoid, semiring and dioid, and go on to show in the book the relevance of these algebraic structures to such classic operations research problems related to graphs and networks ... . recommend this as a book to be added in the libraries of institutions where graduate courses in OR are taught, because it may provide ideas for PhD students and others to explore further the concepts developed in this book ... ." (R Bharath, Journal of the Operational Research Society, Vol. 60, 2009)