## Combinatorial OptimizationCombinatorial Optimization is the process of finding one or more best (optimal) solutions in a well defined discrete problem space. Such problems occur in almost all fields of management as well as in many engineering disciplines. Many businesses and industries use techniques of discrete optimization to improve the efficiency of their operations. The development of new optimization tools, algorithms and new applications of combinatorial optimization to problems arising in industry and business have been provided. The book also contains complete but concise proofs for several deep results. Many references are given at the end of each topic. |

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### Contents

Minimal Spanning Trees in Probability | 1 |

Discrete Optimizaton Problems in the Design of | 21 |

MinMax Problems on Graphs and Communication Networks | 65 |

Semigraphs | 125 |

The Poly tope of Degree Sequences of Hypergraphs | 139 |

Extensions of KonigEgervary Theorem to Matrioids and Bimatroids | 207 |

### Common terms and phrases

adjacent approximation algorithms axiom bandwidth bandwidth problem bipartite graph block broadcast graphs called Cartesian product Cayley graph circuit Combinatorial Communication Networks complete semigraph Computing connected construct convolution defined Definition degree sequence denote diameter Discrete Mathematics Dn(r edge set Example exists facet fault tolerance forwarding index function on subsets given graph G Graph Theory hypercube hypergraphs IEEE independent sets inequality integral interconnection network intersecting Konig labelling Lemma Let G linear location area location updates Math Mathematics matrix matroid matroid rank function maximally independent maximum minimal spanning tree Minimum Broadcast mobility n-tuple node nonnegative NP-complete number of edges number of vertices obtained optimal parallel algorithm parameters path planar graphs polyhedrally tight polymatroid polymatroid rank function principal partition processors proof random result routes semigraph G set function subgraph submodular function supermodular theta graphs threshold graphs traffic twisted cube vector vertex set vertices of G wireless