000 04247nam a22006135i 4500
001 978-0-387-75450-5
003 DE-He213
005 20161121231208.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387754505
_9978-0-387-75450-5
024 7 _a10.1007/978-0-387-75450-5
_2doi
050 4 _aQA402-402.37
050 4 _aT57.6-57.97
072 7 _aKJT
_2bicssc
072 7 _aKJM
_2bicssc
072 7 _aBUS049000
_2bisacsh
072 7 _aBUS042000
_2bisacsh
082 0 4 _a519.6
_223
100 1 _aGondran, Michel.
_eauthor.
245 1 0 _aGraphs, Dioids and Semirings
_h[electronic resource] :
_bNew Models and Algorithms /
_cby Michel Gondran, Michel Minoux.
264 1 _aBoston, MA :
_bSpringer US,
_c2008.
300 _aXX, 388 p. 26 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOperations Research/Computer Science Interfaces,
_x1387-666X ;
_v41
505 0 _aPre-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.
520 _aThe 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 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.
650 0 _aMathematics.
650 0 _aOperations research.
650 0 _aDecision making.
650 0 _aComputer organization.
650 0 _aComputer science
_xMathematics.
650 0 _aMathematical models.
650 0 _aManagement science.
650 0 _aCombinatorics.
650 1 4 _aMathematics.
650 2 4 _aOperations Research, Management Science.
650 2 4 _aComputer Systems Organization and Communication Networks.
650 2 4 _aCombinatorics.
650 2 4 _aOperation Research/Decision Theory.
650 2 4 _aDiscrete Mathematics in Computer Science.
650 2 4 _aMathematical Modeling and Industrial Mathematics.
700 1 _aMinoux, Michel.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387754499
830 0 _aOperations Research/Computer Science Interfaces,
_x1387-666X ;
_v41
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-75450-5
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509968
_d509968