Combinatorial Optimization

This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references.

This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial optimization.

1 Introduction

2 Graphs

3 Linear Programming

4 Linear Programming Algorithms

5 Integer Programming

6 Spanning Trees and Arborescences

7 Shortest Paths

8 Network Flows

9 Minimum Cost Flows

10 Maximum Matchings

11 Weighted Matching

12 b -Matchings and T-Joins

13 Matroids

14 Generalizations of Matroids

15 NP-Completeness

16 Approximation Algorithms

17 The Knapsack Problem

18 Bin-Packing

19 Multicommodity Flows and Edge-Disjoint Paths

20 Network Design Problems

21 The Traveling Salesman Problem

22 Facility Location

About the Author

Bernhard Korte is professor of operations research and director of the Research Institute for Discrete Mathematics at the University of Bonn. He founded the Arithmeum in Bonn and received numerous awards, including a honorary doctoral degree and the “Staatspreis NRW”. His research interests include combinatorial optimization and chip design.

Jens Vygen is professor of discrete mathematics at the University of Bonn and principal investigator of the Hausdorff Center for Mathematics. He also co-authored the textbook “Algorithmic Mathematics” and has served as editor of several books and journals. His research interests include combinatorial optimization and algorithms for chip design.