[share_ebook] Graphs Dioids and Semirings New Models and Algorithms May 2008 eBook-DDU

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.