## 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. |

### 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 assume binary Boolean cache Chapter Chernoff bound choice choose chosen clauses competitiveness coefficient compute Consider constraints contains corresponding define Definition denote deterministic algorithm distribution elements evaluating Exercise expanding graphs expected number expected running finding given graph G hash function independent inequality input integer intersection iteration Las Vegas algorithm least Lemma linear programming lower bound Markov chain martingale min-cut modulo node NP-complete number of edges number of steps O(log O(nē obtain offline online algorithm output pairwise independent partition path perfect matching permutation pointers polynomial Pr[X prime problem processors proof prove quadratic residue random bits random variable random walk randomized algorithm recursive result RNC algorithm S₁ sampling satisfying Section segments Show skip list space square roots sub-tree subset Suppose technique Theorem treap truth assignment uniformly at random upper bound vector verify vertex weight X₁

### Popular passages

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.