Graphs, Dioids and Semirings: New Models and Algorithms

最新推荐文章于 2024-12-15 18:17:47 发布

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最新推荐文章于 2024-12-15 18:17:47 发布

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本文探讨了图论的历史起源及其在计算机科学等应用科学中的关键作用。从欧拉解决著名的哥尼斯堡七桥问题开始，到现代电子计算机普及背景下图论成为不可或缺的学科。本文还介绍了图论与代数结构如半环、双代数之间的深刻联系及其在算法设计中的应用。

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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 C the 'Traveling Salesman Problem' -, is still the subject of active research. Yet, it has been during the last fifty years or sowith the rise of the electronic computersthat 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.

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