Connections in Combinatorial Optimization

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.

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
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
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

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.