Author | Korte, Bernhard. author |
---|---|

Title | Combinatorial Optimization [electronic resource] : Theory and Algorithms / by Bernhard Korte, Jens Vygen |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000 |

Connect to | http://dx.doi.org/10.1007/978-3-662-21708-5 |

Descript | XI, 530 p. online resource |

SUMMARY

Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. It became a subject in its own right about 50 years ago. This book describes the most important ideas, theoretical results, and algoยญ rithms in combinatorial optimization. We have conceived it as an advanced graduยญ ate text which can also be used as an up-to-date reference work for current research. The book includes the essential fundamentals of graph theory, linear and integer programming, and complexity theory. It covers classical topics in combinatorial optimization as well as very recent ones. The emphasis is on theoretical results and algorithms with provably good performance. Applications and heuristics are mentioned only occasionally. Combinatorial optimization has its roots in combinatorics, operations research, and theoretical computer science. A main motivation is that thousands of real-life problems can be formulated as abstract combinatorial optimization problems. We focus on the detailed study of classical problems which occur in many different contexts, together with the underlying theory. Most combinatorial optimization problems can be formulated naturally in terms of graphs and as (integer) linear programs. Therefore this book starts, after an introduction, by reviewing basic graph theory and proving those results in linear and integer programming which are most relevant for combinatorial optimization

CONTENT

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 -- Notation Index -- Author Index

Mathematics
Computer science -- Mathematics
Calculus of variations
Combinatorics
Mathematics
Combinatorics
Calculus of Variations and Optimal Control; Optimization
Mathematics of Computing