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130626  eng 
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a 9780387754505

100 
1 

a Gondran, Michel

245 
0 
0 
a Graphs, Dioids and Semirings
h Elektronische Ressource
b New Models and Algorithms
c by Michel Gondran, Michel Minoux

250 


a 1st ed. 2008

260 


a New York, NY
b Springer US
c 2008, 2008

300 


a XX, 388 p. 26 illus
b online resource

505 
0 

a PreSemirings, Semirings and Dioids  Combinatorial Properties of (Pre)Semirings  Topology on Ordered Sets: Topological Dioids  Solving Linear Systems in Dioids  Linear Dependence and Independence in SemiModules and Moduloids  Eigenvalues and Eigenvectors of Endomorphisms  Dioids and Nonlinear Analysis  Collected Examples of Monoids, (Pre)Semirings and Dioids

653 


a Operations Research, Management Science

653 


a Operations research

653 


a Computer science / Mathematics

653 


a Management science

653 


a Discrete Mathematics in Computer Science

653 


a Computer networks

653 


a Computer Engineering and Networks

653 


a Mathematical Modeling and Industrial Mathematics

653 


a Discrete Mathematics

653 


a Computer engineering

653 


a Discrete mathematics

653 


a Operations Research and Decision Theory

653 


a Mathematical models

700 
1 

a Minoux, Michel
e [author]

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Operations Research/Computer Science Interfaces Series

028 
5 
0 
a 10.1007/9780387754505

856 
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u https://doi.org/10.1007/9780387754505?nosfx=y
x Verlag
3 Volltext

082 
0 

a 003

520 


a The origins of Graph Theory date back to Euler (1736) with the solution of the celebrated 'Koenigsberg Bridges Problem'; and to Hamilton with the famous 'Trip around the World' game (1859), stating for the first time a problem which, in its most recent version – the 'Traveling Salesman Problem' , is still the subject of active research. Yet, it has been during the last fifty years or so—with the rise of the electronic computers—that Graph theory has become an indispensable discipline in terms of the number and importance of its applications across the Applied Sciences. Graph theory has been especially central to Theoretical and Algorithmic Computer Science, and Automatic Control, Systems Optimization, Economy and Operations Research, Data Analysis in the Engineering Sciences. Close connections between graphs and algebraic structures have been widely used in the analysis and implementation of efficient algorithms for many problems, for example: transportation network optimization, telecommunication network optimization and planning, optimization in scheduling and production systems, etc. 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 problemsolving 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
