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Zusatztext The title of the book is wisely chosen: it deals, among other subjects, with graph connectivity, and it provides connections between graph theoretical results and underlying combinatorial structures...The book is readable for students, researchers, possibly also practitioners. Informationen zum Autor András Frank is the founder and head of the MTA-ELTE Egerváry Research Group (EGRES) at Eötvös University. He was head of the Department of Operations Research at Eötvös University between 1995 and 2009. In 2002, he was awarded the Tibor Szele Prize by the János Bolyai Mathematical Society, and in 2009, the Cultural Ministry of Hungary awarded him the Szent-Gyorgyi Albert Prize. Klappentext Graph connectivities and submodular functions are two widely applied and fast developing fields of combinatorial optimization. This book not only includes the most recent results, but also highlights several surprising connections between diverse topics within combinatorial optimization. It offers a unified treatment of developments in the concepts and algorithmic methods of the area, starting from basic results on graphs, matroids and polyhedral combinatorics,through the advanced topics of connectivity issues of graphs and networks, to the abstract theory and applications of submodular optimization. Difficult theorems and algorithms are made accessible to graduate students in mathematics, computer science, operations research, informatics and communication.The book is not only a rich source of elegant material for an advanced course in combinatorial optimization, but it also serves as a reference for established researchers by providing efficient tools for applied areas like infocommunication, electric networks and structural rigidity. Zusammenfassung Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers. Inhaltsverzeichnis Preface PART I - Basic Combinatorial Optimization 1: Elements of graphs and hypergraphs 2: Connectivity, paths, and matchings 3: Elements of network optimization 4: Elements of polyhedral combinatorics 5: Elements of matroid theory PART II - Higher-Order Connections 6: Efficient algorithms for flows and cuts 7: Structure and representations of cuts 8: The splitting off operation and constructive characterizations 9: Orientations of graphs and hypergraphs 10: Trees and arborescences: packing and covering 11: Preserving and improving connections PART III - Semimodular Optimization 12: Setting the stage: aspects and approaches 13: Matroid optimization 14: Generalized polymatroids 15: Relaxing semimodularity 16: Submodular flows 17: Covering supermodular functions by digraphs Solutions to selected problems Bibliography Index ...
