## Probability and Computing: Randomized Algorithms and Probabilistic AnalysisRandomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool. |

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User Review - Flag as inappropriate

Excellent book. Lower level than Motwani Raghavan; so, good for raw beginners. Section on routing on butterfly network not clear to me. Other parts were fine.

### Contents

II | 1 |

III | 3 |

IV | 8 |

V | 12 |

VI | 14 |

VII | 20 |

VIII | 22 |

IX | 23 |

LXXVIII | 177 |

LXXIX | 182 |

LXXX | 188 |

LXXXI | 191 |

LXXXII | 193 |

LXXXIII | 194 |

LXXXIV | 196 |

LXXXV | 197 |

X | 25 |

XI | 26 |

XII | 30 |

XIII | 32 |

XIV | 34 |

XV | 38 |

XVI | 44 |

XVII | 45 |

XVIII | 48 |

XX | 50 |

XXI | 52 |

XXII | 53 |

XXIII | 54 |

XXIV | 57 |

XXV | 61 |

XXVI | 63 |

XXVIII | 67 |

XXX | 69 |

XXXI | 71 |

XXXII | 72 |

XXXIII | 73 |

XXXIV | 78 |

XXXV | 83 |

XXXVI | 90 |

XXXVII | 92 |

XXXVIII | 93 |

XXXIX | 94 |

XL | 98 |

XLI | 99 |

XLII | 104 |

XLIII | 106 |

XLIV | 107 |

XLV | 109 |

XLVI | 111 |

XLVII | 112 |

XLVIII | 113 |

XLIX | 119 |

L | 124 |

LI | 126 |

LII | 128 |

LIII | 129 |

LIV | 130 |

LV | 131 |

LVI | 133 |

LVIII | 134 |

LX | 135 |

LXI | 136 |

LXII | 138 |

LXIII | 141 |

LXIV | 142 |

LXVI | 143 |

LXVII | 146 |

LXVIII | 148 |

LXIX | 153 |

LXX | 156 |

LXXI | 159 |

LXXII | 163 |

LXXIII | 166 |

LXXIV | 167 |

LXXV | 173 |

LXXVI | 174 |

LXXVII | 176 |

LXXXVI | 199 |

LXXXVII | 201 |

LXXXVIII | 204 |

LXXXIX | 205 |

XC | 207 |

XCI | 210 |

XCII | 212 |

XCIII | 213 |

XCIV | 216 |

XCVI | 219 |

XCVII | 225 |

XCVIII | 228 |

XCIX | 230 |

C | 234 |

CI | 237 |

CII | 245 |

CIII | 252 |

CIV | 255 |

CVI | 257 |

CVII | 259 |

CVIII | 263 |

CIX | 265 |

CX | 267 |

CXI | 270 |

CXII | 271 |

CXIII | 274 |

CXIV | 275 |

CXV | 276 |

CXVI | 277 |

CXVII | 278 |

CXVIII | 281 |

CXIX | 282 |

CXX | 286 |

CXXI | 289 |

CXXII | 295 |

CXXIII | 297 |

CXXIV | 299 |

CXXV | 300 |

CXXVI | 303 |

CXXVII | 305 |

CXXVIII | 307 |

CXXIX | 308 |

CXXXI | 309 |

CXXXII | 314 |

CXXXIII | 315 |

CXXXIV | 316 |

CXXXV | 317 |

CXXXVI | 318 |

CXXXVII | 319 |

CXXXVIII | 321 |

CXXXIX | 323 |

CXL | 324 |

CXLI | 326 |

CXLII | 328 |

CXLIII | 333 |

CXLIV | 336 |

CXLV | 341 |

CXLVI | 344 |

CXLVIII | 345 |

CL | 349 |

350 | |

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### Common terms and phrases

apply assume binomial bins Bloom filter chapter Chebyshev's inequality Chernoff bound choose chosen independently chosen uniformly clause codeword coin flips color compute consider constant coupling coupon decoding function Definition elements entropy event example Exercise expected number exponentially distributed fair coin finite geometric random variable given gives graph G Hamiltonian cycle hash functions heads Hence high probability independent sets independently and uniformly input integer Lemma linearity of expectations log2 Markov chain Markov's inequality martingale maximum load node number of balls number of bits number of steps obtain output packet pair pairwise independent path permutation phase player Poisson process polynomial Pr(X probability 1/2 problem Proof prove queue Quicksort random graph random walk randomized algorithm randomly routing sample space satisfying assignment sequence stationary distribution Suppose Theorem total number uniform uniformly at random unused-edges list upper bound Var[X variation distance vertex vertices wins yields