Probability and Computing: Randomized Algorithms and Probabilistic AnalysisCambridge University Press, 31 sty 2005 - 352 Randomization 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. |
Spis treści
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 | |
Inne wydania - Wyświetl wszystko
Probability and Computing: Randomized Algorithms and Probabilistic Analysis Michael Mitzenmacher,Eli Upfal Ograniczony podgląd - 2005 |
Kluczowe wyrazy i wyrażenia
apply assume binomial bins Bloom filter Chebyshev's inequality Chernoff bound choose chosen independently chosen uniformly clause codeword coin flips color compute consider constant coupling coupon d₁ Definition elements event example Exercise expected number exponentially distributed finite given gives Hamiltonian cycle hash functions Hence high probability independent sets independently and uniformly input integer least Lemma linearity of expectations log2 Markov chain Markov's inequality martingale maximum load node number of balls number of bits obtain output packet pair pairwise independent parameter path permutation phase player Poisson process polynomial Pr(E Pr(X Pr(Y probabilistic probability 1/2 problem Proof prove queue Quicksort random graph random walk randomized algorithm routing sample space satisfying assignment sequence stationary distribution Suppose Theorem total number uniform uniformly at random upper bound Var[X variation distance vertex vertices wins X₁ Y₁ yields