## Randomized AlgorithmsFor many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students. |

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I am getting so frustrated after reading this book, only mathematical intuitions are given and explain in a very bad manner. please try to make it more readable and simplify the proves as much as you can so that we could understand it easily. Even the outline is not written in well manner.

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### Contents

I | ix |

II | 1 |

III | 3 |

IV | 28 |

V | 43 |

VI | 67 |

VII | 101 |

VIII | 127 |

X | 195 |

XI | 197 |

XII | 234 |

XIII | 278 |

XIV | 306 |

XV | 335 |

XVI | 368 |

XVII | 392 |

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### Common terms and phrases

adversary analysis apply assignment assume bits bound called Chapter choice choose chosen clauses complexity compute connected Consider constant constraints construction contains corresponding cost define Definition denote described determine distinct distribution easy edges efficient elements equal error exactly example Exercise exists expected expected number fact factor finding function given gives graph hash idea implies independent input instance integer known least Lemma length linear lower Markov matrix min-cut multiplication node Note observation obtain operation partition path perfect matching perform permutation polynomial positive possible prime probability problem processors proof prove random variable randomized algorithm refer request requires result root round running sampling satisfying scheme sequence Show solution space step Suppose technique Theorem tree uniformly vector verify vertex vertices weight

### Popular passages

Page 463 - JP Schmidt, A. Siegel, and A. Srinivasan. Chernoff-Hoeffding bounds for applications with limited independence. In Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 331-340, 1993.

Page 451 - U. Manber and G. Myers. Suffix arrays: A new method for on-line string searches. In Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 319-327, 1990.

Page 452 - KL Clarkson. A Las Vegas algorithm for linear programming when the dimension is small. In Proc. 29th Annu. IEEE Sympos. Found. Comput. Sei., pages 452-456, 1988. [21] KL Clarkson and PW Shor. Applications of random sampling in computational geometry, II.