## Randomized AlgorithmsFor many applications, a randomized algorithm is either the simplest or the fastest algorithm available, and sometimes both. This book introduces the basic concepts in the design and analysis of randomized algorithms. The first part of the text presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications. Algorithmic examples are also given to illustrate the use of each tool in a concrete setting. In the second part of the book, each chapter focuses on an important area to which randomized algorithms can be applied, providing a comprehensive and representative selection of the algorithms that might be used in each of these areas. Although written primarily as a text for advanced undergraduates and graduate students, this book should also prove invaluable as a reference for professionals and researchers. |

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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 |

XIV | 278 |

XV | 306 |

XVI | 335 |

XVII | 368 |

XVIII | 392 |

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### Common terms and phrases

adversary analysis apply assignment assume bits bound called Chapter choice choose chosen clauses complete 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 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.