Iterative Methods in Combinatorial Optimization

Erscheinungsjahr 2011
ISBN: 978-1-107-00751-2
Verlag: Cambridge University Press

Buch, Englisch, Band 46, 254 Seiten, HC gerader Rücken kaschiert, Format (B × H): 157 mm x 235 mm, Gewicht: 573 g

Reihe: Cambridge Texts in Applied Mathematics

• Presents a unified way of looking at several problems
• Offers new ways of deriving classical results in optimization
• Provides extensions to hard variants of classical problems
• Offers elementary presentation appealing to a broad mathematically interested audience
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.

Autoren/Hrsg.

Lau, Lap-Chi

Ravi, R.

Singh, Mohit

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Singh, Mohit
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.

Lau, Lap-Chi
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.

Ravi, R.
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.