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＜電子ブック＞
CATBox : An Interactive Course in Combinatorial Optimization / by Winfried Hochstättler, Alexander Schliep

版	1st ed. 2010.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2010
本文言語	英語
大きさ	XII, 190 p. 36 illus : online resource
著者標目	*Hochstättler, Winfried author Schliep, Alexander author SpringerLink (Online service)
件　名	LCSH:Discrete mathematics LCSH:Game theory LCSH:Mathematical optimization LCSH:Operations research LCSH:Management science LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Discrete Mathematics FREE:Game Theory FREE:Optimization FREE:Operations Research, Management Science FREE:Discrete Mathematics in Computer Science
一般注記	Discrete Problems from Applications -- Basics, Notation and Data Structures -- Minimum Spanning Trees -- Linear Programming Duality -- Shortest Paths -- Maximal Flows -- Minimum-Cost Flows -- Matching -- Weighted Matching Graph algorithms are easy to visualize and indeed there already exists a variety of packages and programs to animate the dynamics when solving problems from graph theory. Still, and somewhat surprisingly, it can be difficult to understand the ideas behind the algorithm from the dynamic display alone. CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. He or she can set breakpoints, proceed in single steps and trace into subroutines. The graph, and additional auxiliary graphs like residual networks, are displayed and provide visual feedback. The course book, intended for readers at advanced undergraduate or graduate level, introduces the ideas and discusses the mathematical background necessary for understanding and verifying the correctness of the algorithms and their complexity. Computer exercises and examples replace the usual static pictures of algorithm dynamics. For this volume we have chosen solely algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows as well as weighted and unweighted matchings both for bipartite and non-bipartite graphs. We consider non-bipartite weighted matching, in particular in the geometrical case, a highlight of combinatorial optimization. In order to enable the reader to fully enjoy the beauty of the primal-dual solution algorithm for weighted matching, we present all mathematical material not only from the point of view of graph theory, but also with an emphasis on linear programming and its duality. This yields insightful and aesthetically pleasing pictures for matchings, but also for minimum spanning trees. You can find more information at http://schliep.org/CATBox/ HTTP:URL=https://doi.org/10.1007/978-3-642-03822-8

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