## 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 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, balls and bins models, the probabilistic method, and Markov chains. In the second half, the authors delve into more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods, coupling, martingales, and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool. |

### What people are saying - Write a review

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 |

V | 3 |

VI | 8 |

VII | 12 |

VIII | 14 |

IX | 20 |

XI | 22 |

XII | 23 |

LXXXIX | 177 |

XC | 182 |

XCI | 188 |

XCIV | 191 |

XCV | 193 |

XCVI | 194 |

XCVII | 196 |

XCVIII | 197 |

XIII | 25 |

XIV | 26 |

XV | 30 |

XVI | 32 |

XVII | 34 |

XVIII | 38 |

XIX | 44 |

XXII | 45 |

XXIII | 48 |

XXIV | 50 |

XXV | 52 |

XXVI | 53 |

XXVII | 54 |

XXVIII | 57 |

XXIX | 61 |

XXXII | 63 |

XXXIII | 67 |

XXXV | 69 |

XXXVI | 71 |

XXXVII | 72 |

XXXVIII | 73 |

XXXIX | 78 |

XL | 83 |

XLI | 90 |

XLIV | 92 |

XLV | 93 |

XLVI | 94 |

XLVII | 98 |

XLVIII | 99 |

XLIX | 104 |

L | 106 |

LI | 107 |

LII | 109 |

LIII | 111 |

LIV | 112 |

LV | 113 |

LVI | 119 |

LVII | 124 |

LVIII | 126 |

LXI | 128 |

LXII | 129 |

LXIII | 130 |

LXIV | 131 |

LXV | 133 |

LXVII | 134 |

LXIX | 135 |

LXX | 136 |

LXXI | 138 |

LXXII | 141 |

LXXIII | 142 |

LXXV | 143 |

LXXVI | 146 |

LXXVII | 148 |

LXXVIII | 153 |

LXXXI | 156 |

LXXXII | 159 |

LXXXIII | 163 |

LXXXIV | 166 |

LXXXV | 167 |

LXXXVI | 173 |

LXXXVII | 174 |

LXXXVIII | 176 |

XCIX | 199 |

C | 201 |

CI | 204 |

CII | 205 |

CIII | 207 |

CIV | 210 |

CV | 212 |

CVI | 213 |

CVII | 216 |

CIX | 219 |

CX | 225 |

CXI | 228 |

CXII | 230 |

CXIII | 234 |

CXIV | 237 |

CXV | 245 |

CXVI | 252 |

CXVIII | 255 |

CXX | 257 |

CXXI | 259 |

CXXII | 263 |

CXXIII | 265 |

CXXIV | 267 |

CXXV | 270 |

CXXVI | 271 |

CXXIX | 274 |

CXXX | 275 |

CXXXI | 276 |

CXXXII | 277 |

CXXXIII | 278 |

CXXXIV | 281 |

CXXXV | 282 |

CXXXVI | 286 |

CXXXVII | 289 |

CXXXVIII | 295 |

CXXXIX | 297 |

CXL | 299 |

CXLI | 300 |

CXLII | 303 |

CXLIII | 305 |

CXLIV | 307 |

CXLV | 308 |

CXLVII | 309 |

CXLVIII | 314 |

CLI | 315 |

CLII | 316 |

CLIII | 317 |

CLIV | 318 |

CLV | 319 |

CLVI | 321 |

CLVII | 323 |

CLVIII | 324 |

CLIX | 326 |

CLX | 328 |

CLXI | 333 |

CLXII | 336 |

CLXIII | 341 |

CLXIV | 344 |

CLXVI | 345 |

CLXVIII | 349 |

350 | |

### Other editions - View all

### Common terms and phrases

algorithm analysis apply approach approximation argument arrival assignment assume balls bins bits bound chapter Chernoff bound choices choose clause coin color compute conditional connected consider constant corresponding count coupling customers defined Definition determine edges elements equal event exactly example Exercise exists expected expected number exponential fact finite flips given gives graph hash functions heads Hence holds independent independent sets inequality input least Lemma load Markov chain maximum mean method move node obtain otherwise output packet pair parameter path phase placed Poisson polynomial positive possible Pr(X probability problem Proof prove queue random variable received represent result routing running sample satisfying sequence simple sorted space specific stationary distribution step sufficiently Suppose takes Theorem transition uniform uniformly at random vertex vertices wins yields