## Networks in Action: Text and Computer Exercises in Network OptimizationOne of the most well-known of all network optimization problems is the shortest path problem, where a shortest connection between two locations in a road network is to be found. This problem is the basis of route planners in vehicles and on the Internet. Networks are very common structures; they consist primarily of a ?nite number of locations (points, nodes), together with a number of links (edges, arcs, connections) between the locations. Very often a certain number is attached to the links, expressing the distance or the cost between the end points of that connection. Networks occur in an extremely wide range of applications, among them are: road networks; cable networks; human relations networks; project scheduling networks; production networks; distribution networks; neural networks; networks of atoms in molecules. In all these cases there are “objects” and “relations” between the objects. A n- work optimization problem is actually nothing else than the problem of ?nding a subset of the objects and the relations, such that a certain optimization objective is satis?ed. |

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### Contents

1 | |

3 | |

References with Comments | 11 |

Shortest Paths | 17 |

Minimum Spanning Trees | 37 |

Network Flows | 61 |

Matchings | 87 |

Facility Location | 116 |

Cyclic Routing on Networks | 143 |

181 | |

Erratum | 183 |

183 | |

### Other editions - View all

Networks in Action: Text and Computer Exercises in Network Optimization Gerard Sierksma,Diptesh Ghosh No preview available - 2009 |

Networks in Action: Text and Computer Exercises in Network Optimization Gerard Sierksma,Diptesh Ghosh No preview available - 2012 |

### Common terms and phrases

arcs assignment bottleneck branch and bound building cable laying sites cable network called capacitated facility location capacity Chinese postman problem Combinatorial Optimization components connected Constraint 4.1 decision variables denoted departments depot destination node Dijkstra’s algorithm distance employees ensure exactly once example facility location problem greedy heuristic GTC wants Hamiltonian path problem help desk iteration kilometers label library facilities linear programming formulation logistical Management matrix Maximize maximum cardinality matching maximum flow maximum flow problem Minimize minimum spanning tree network flow problem network in Figure network optimization number of edges Operations Research optimal solution output p-center problem pair problem described represented road network road segment routing problems set of constraints shortest path problem shown in Figure Sierksma similar constraints solve source node spanning tree problem spools subproblem subset subtour Table technician traveling salesman problem uncapacitated units warehouse