## Handbooks in Operations Research and Management Science: Discrete OptimizationThe chapters of this Handbook volume cover nine main topics that are representative of recent theoretical and algorithmic developments in the field. In addition to the nine papers that present the state of the art, there is an article on the early history of the field. The handbook will be a useful reference to experts in the field as well as students and others who want to learn about discrete optimization. |

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### Indhold

1 | |

Chapter 2 Computational Integer Programming and Cutting Planes | 69 |

Chapter 3 The Structure of Group Relaxations | 123 |

Chapter 4 Integer Programming Lattices and Results in Fixed Dimension | 171 |

Chapter 5 Primal Integer Programming | 245 |

Chapter 6 Balanced Matrices | 277 |

### Almindelige termer og sætninger

algebraic applied approximation algorithm augmenting path balanced basis reduction algorithm Benders binary bipartite graph called columns combinatorial optimization cone cone(A constraint programming contains convex hull cutting planes decomposition defined denote dual edge exists feasible solution finite flow given graph G group relaxations Hence hyperplane implies IPA,c iteration Iwata Journal lattice Lemma linear programming Lov asz lower bound LP relaxation Mathematical Programming matrix matroid max-cut maximum method minimal mixed integer programming nodes nonnegative obtained Operations Research optimal solution optimization problem optimum orthogonal polyhedra polyhedron polymatroid polynomial polytope primal programming problem proof random reduced satisfies Schrijver Section semidefinite programming semidefinite relaxation SFM algorithms shortest vector simplex SMIP solve stable set standard pair submodular function subproblem subset Theorem traveling salesman problem triangulation unimodular valid inequalities variables vertex vertices Wolsey

### Populære passager

Side 26 - The cultural lag of economic thought in the application of mathematical methods is strikingly illustrated by the fact that linear graphs are making their entrance into transportation theory just about a century after they were first studied in relation to electrical networks, although organized transportation systems are much older than the study of electricity.

Side 29 - Consider a network (eg. rail, road, communication network) connecting two given points by way of a number of intermediate points, where each link of the network has a number assigned to it representing its capacity. Assuming a steady state condition, find a maximal flow from one given point to the other.

Side 2 - Department of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.

Side 54 - Ball also discusses the relationships between the Hamiltonian Game and other unicursal problems. Konig2 discusses some of these same problems under the heading Hamiltonian Lines. I am indebted to AW Tucker for calling these connections to my attention, in 1937, when I was struggling with the problem in connection with a schoolbus routing study in New Jersey.