Connections in Combinatorial Optimization

• A unified treatment of the development of ideas and methods of the area
• Richly illustrates how concrete results naturally give rise to the introduction of abstract notions and how results concerning these notions can be applied in special cases to get more sophisticated concrete results
• Difficult theorems and algorithms are made accessible and easily digestible
• Demonstrates several surprising connections between diverse topics of combinatorial optimization, such as connectivity issues of networks and submodular optimization
• Includes the most up to date results from the field

Readership: Graduates and researchers in mathematics, computer science, informatics, and communication that rely on methods of combinatorial optimization.

András Frank, MTA-ELTE Egerváry Research Group, Institute of Mathematics, Eötvös Loránd University, Budapest

"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." - Mathematical Reviews

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