## Combinatorial OptimizationA complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade. Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include: * Network flow problems * Optimal matching * Integrality of polyhedra * Matroids * NP-completeness Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come. |

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### Contents

1 | |

9 | |

3 Maximum Flow Problems | 37 |

4 MinimumCost Flow Problems | 91 |

5 Optimal Matchings | 127 |

6 Integrality of Polyhedra | 199 |

7 The Traveling Salesman Problem | 241 |

8 Matroids | 273 |

9 NP and NPCompleteness | 309 |

APPENDIX A Linear Programming | 325 |

337 | |

347 | |

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### Common terms and phrases

augmenting path b-matching bipartite graph characteristic vector choose combinatorial common independent set compute constraints convex hull corresponding cost cutting-plane deﬁne deﬁnition delete denote digraph digraph G dual solution edge-set Edmonds example Exercise exists feasible solution Figure ﬁnd ﬁrst follows Ford’s Algorithm given graph G Greedy Algorithm implies inequality integral vectors iterations Lemma Let G linear linear-programming problem lower bound matching algorithm matching of G matching problem matrix Matroid Intersection maximum ﬂow problem maximum matching maximum-weight Minimize minimum cut minimum-cost ﬂow problem Moreover node nodes of G nonnegative obtain odd circuit optimal solution optimal value P-complete pair perfect matching polyhedron polynomial polytope Primal-Dual Algorithm problem of ﬁnding proof Proposition Prove pseudonode replace result satisﬁes shortest path problem solve spanning tree step subgraph subset Suppose Theorem totally unimodular tour traveling salesman problem tree solution triangle inequality undirected graph weight