## Topics in combinatorial optimization |

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### Contents

Optimal Constrained Cycles in Graphs | 47 |

Complexity of Combinatorial Computations | 87 |

Some Aspects of Duality in Combinatorial Optimization | 109 |

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### Common terms and phrases

Algorithm 3.1 arc i,j associated asymptotic optimization augmenting path average search length basic assignment basic cycles Branch and Bound Branch Search branching function combinatorial optimization complexity computation consider constraint rates contain corresponding defined deterministic duality dynamic programming E.L. Lawler element elementary cycles equations example exists feasible solution finite given graph G greedy algorithm heuristic independent set integer label locations lower bound Markov chains matrix matroid intersection Max-Flow Min-Cut Theorem method minimal monotone negative cycle network flow node nondeterministic Turing machine NP-complete number of iterations obtained optimal cycle optimal solution partitioning properties Periodic Optimization problem polynomial bounded polynomial-bounded positive cover possible Problem 1.1 problem of finding problem reduction search tree selfloops sequence sequential decision process sets of solutions shortest path solution class step subgraph subset terminal Theorem theory traveling salesman problem Turing machine unfeasibility threshold upper bound variables vector vertex