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.
Table of Contents:
1. Introduction2. Preliminaries3. Matching and vertex cover in bipartite graphs4. Spanning trees5. Matroids6. Arborescence and rooted connectivity7. Submodular flows and applications8. Network matrices9. Matchings10. Network design11. Constrained optimization problems12. Cut problems13. Iterative relaxation: early and recent examples14. Summary.
|Title:||Iterative Methods in Combinatorial Optimization||Publisher:||Cambridge University Press|
|Author:||Lap Chi Lau, R Ravi, Mohit Singh|
|Edition:||Ebook 1 , PDF|
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