Iterative Methods in Combinatorial Optimization

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Lap Chi Lau (The Chinese University of Hong Kong) R. Ravi (Carnegie Mellon University, Pennsylvania)

Iterative Methods in Combinatorial Optimization

Lap Chi Lau (The Chinese University of Hong Kong), R. Ravi (Carnegie Mellon University, Pennsylvania), Mohit Singh (McGill University, Montréal)

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English

Cambridge University Press
18 April 2011

Optimisation; Combinatorics & graph theory; Algorithms & data structures

Series: Cambridge Texts in Applied Mathematics

With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

By: Lap Chi Lau (The Chinese University of Hong Kong), R. Ravi (Carnegie Mellon University, Pennsylvania), Mohit Singh (McGill University, Montréal)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 46
Dimensions: Height: 229mm, Width: 153mm, Spine: 15mm
Weight: 360g
ISBN: 9780521189439
ISBN 10: 0521189438
Series: Cambridge Texts in Applied Mathematics
Pages: 256
Publication Date: 18 April 2011
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Introduction; 2. Preliminaries; 3. Matching and vertex cover in bipartite graphs; 4. Spanning trees; 5. Matroids; 6. Arborescence and rooted connectivity; 7. Submodular flows and applications; 8. Network matrices; 9. Matchings; 10. Network design; 11. Constrained optimization problems; 12. Cut problems; 13. Iterative relaxation: early and recent examples; 14. Summary.

Lap-Chi Lau is an Assistant Professor in the Department of Computer Science and Engineering at The Chinese University of Hong Kong. Lap-Chi's main research interests are in combinatorial optimization and graph algorithms. His paper on Steiner tree packing was given the Machtey award in the IEEE Foundations of Computer Science Conference. His Ph.D. thesis was awarded the Doctoral Prize from the Canadian Mathematical Society and a Doctoral Prize from the Natural Sciences and Engineering Research Council of Canada. R. Ravi is Carnegie Bosch Professor of Operations Research and Computer Science at Carnegie Mellon University. Ravi's main research interests are in combinatorial optimization (particularly in approximation algorithms), computational molecular biology and electronic commerce. He is currently on the editorial boards of Management Science and the ACM Transactions on Algorithms. Mohit Singh is an Assistant Professor in the School of Computer Science, McGill University. He completed his Ph.D. in 2008 at the Tepper School of Business, Carnegie Mellon University, where his advisor was Professor R. Ravi. His thesis was awarded the Tucker prize by the Mathematical Programming Society. His research interests include approximation algorithms, combinatorial optimization and studying models that deal with uncertainty in data.