Network Flow Algorithms

Network flow theory has been used across a number of disciplines, including theoretical computer science, operations research, and discrete math, to model not only problems in the transportation of goods and information, but also a wide range of applications from image segmentation problems in computer vision to deciding when a baseball team has been eliminated from contention. This graduate text and reference presents a succinct, unified view of a wide variety of efficient combinatorial algorithms for network flow problems, including many results not found in other books. It covers maximum flows, minimum-cost flows, generalized flows, multicommodity flows, and global minimum cuts and also presents recent work on computing electrical flows along with recent applications of these flows to classical problems in network flow theory.

1. Preliminaries: shortest path algorithms; 2. Maximum flow algorithms; 3. Global minimum cut algorithms; 4. More maximum flow algorithms; 5. Minimum-cost circulation algorithms; 6. Generalized flow algorithms; 7. Multicommodity flow algorithms; 8. Electrical flow algorithms; 9. Open questions.

David P. Williamson is a Professor at Cornell University, New York, in the School of Operations Research and Information Engineering. He has won several awards for his work in discrete optimization, including the 2000 Fulkerson Prize, sponsored by the American Mathematical Society and the Mathematical Programming Society. His previous book, The Design of Approximation Algorithms (Cambridge, 2011), co-authored with David B. Shmoys, won the 2013 INFORMS Lanchester Prize. He has served on several editor boards, and was editor-in-chief of the SIAM Journal on Discrete Mathematics. He is a Fellow of the ACM and of SIAM.