## Algorithms and complexity |

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### Contents

Mathematical Preliminaries | 8 |

Recursive Algorithms | 48 |

The Network Flow Problem | 105 |

Copyright | |

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### Common terms and phrases

binomial coefficients bipartite graph blocking flow calculate certificate choose chromatic number clauses complexity composite computational problem decision problem denote describe discuss divisor edges of G elements equation Euclidean algorithm exactly example Exercises for section extended Euclidean algorithm factorization fast algorithm Fast Fourier Transform flow augmenting path flow function Ford-Fulkerson algorithm Fourier transform graph G graph-coloring Hence instance integer labeled graphs largest independent set layered network lemma matrices maximum flow maxsetl method modulo multiplications of numbers network flow network flow problem NP-complete NP-complete problems nth roots number of bits number of edges pair polynomial polynomial-time positive integers prime number primitive root procedure proper colorings prove pseudoprimality test Quicksort random recursive algorithm recursive calls roots of unity sequence set of vertices shown in Fig solution solve splitter step subsets Suppose tree true Turing machine values variables vertex vertices of G