Iterative Methods in Combinatorial Optimization

A simple, powerful method that is iterative and useful in a variety of settings for exact and approximate optimization.

Lap Chi Lau (Author), R. Ravi (Author), Mohit Singh (Author)

9781107007512, Cambridge University Press

Hardback, published 18 April 2011

254 pages, 44 b/w illus. 102 exercises
23.5 x 15.9 x 1.8 cm, 0.48 kg

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.

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.

Subject Areas: Algorithms & data structures [UMB], Optimization [PBU]