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- |[[File:Probability and Computing. 2nd Edition cover.jpg|border|143x143px]]|| :'''''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis ...2 KB (231 words) - 06:43, 14 September 2023
- In [[computing]] science common monoids include [[addition]], [[multiplication]], or, and. ...729 bytes (116 words) - 19:01, 14 June 2016
- ...]</math> by the definition of expectations. There is also a smarter way of computing <math>\mathbf{E}[X]</math>, by using indicators and the linearity of expec ...3 KB (445 words) - 02:33, 19 July 2011
- * '''[MU]''' Michael Mitzenmacher and Eli Upfal. ''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. Cambridge University P ...2 KB (132 words) - 11:58, 11 January 2010
- == Computing == In [[computing]], the colon [[character (computing)|character]] is represented by [[ASCII]] code 58, and is located at [[Unico ...5 KB (834 words) - 09:40, 24 August 2017
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...1 KB (152 words) - 13:53, 5 September 2022
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...1 KB (155 words) - 13:59, 5 September 2022
- | title = A method for computing all maximally general rules in attribute-value systems | title = Induction of classification rules by granular computing ...5 KB (563 words) - 09:09, 4 February 2016
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...1 KB (159 words) - 08:13, 1 August 2017
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...1 KB (159 words) - 00:15, 2 September 2019
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...1 KB (159 words) - 01:48, 31 August 2016
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...1 KB (159 words) - 05:43, 3 September 2018
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...2 KB (164 words) - 15:02, 22 February 2013
- ...,a_2,\ldots,a_r</math>. Generalize the principle of inclusion-exclusion by computing <math>N_m</math> as the following form ...2 KB (227 words) - 12:38, 3 November 2015
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...2 KB (177 words) - 04:10, 17 February 2014
- * [https://arxiv.org/abs/1907.09415 Ronald de Wolf. Quantum Computing: Lecture Notes.] ...2 KB (222 words) - 06:09, 21 February 2022
- ...y big). There exist methods of fast division by <math>x - a</math>, so the computing the remainder could be easier than the whole function. ...1 KB (269 words) - 18:04, 4 May 2016
- :'''''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'''''. ...3 KB (240 words) - 14:31, 21 July 2011
- * [https://arxiv.org/abs/1907.09415 Ronald de Wolf. Quantum Computing: Lecture Notes. 19 Jul 2019] ...2 KB (234 words) - 07:58, 12 September 2019
- ...1.43.3535 The accuracy of floating point summation]", ''SIAM J. Scientific Computing'' '''14''' (4), 783–799 (1993). ...2 KB (344 words) - 13:31, 21 July 2017
- *Let <math>F_C = F_A \and F_B</math> be the Bloom filter formed by computing the bitwise AND of <math>F_A</math> and <math>F_B</math>. Argue that <math> ...2 KB (406 words) - 14:53, 22 September 2018
- = Computing Graph Expansion = ...can be verified in poly-time. However, there is no efficient algorithm for computing the <math>\phi(G)</math> unless '''NP'''='''P'''. ...8 KB (1,407 words) - 02:23, 25 July 2011
- ...on algorithms for counting and sampling problems. Typical problems include computing marginal probabilities and expectations of random variables, the evaluation :何昆：Kun HE received his Ph.D. degree from the Institute of Computing Technology, Chinese Academy of Sciences in 2019. Currently he is a postdoct ...20 KB (1,328 words) - 14:52, 20 November 2020
- * [https://arxiv.org/abs/1907.09415 Ronald de Wolf. Quantum Computing: Lecture Notes.] ...4 KB (379 words) - 12:06, 27 September 2021
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...4 KB (690 words) - 07:14, 14 October 2019
- Besides directly computing the probability <math>\Pr[X\ge t]</math>, we want to have some general way ...3 KB (541 words) - 15:18, 21 July 2011
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...3 KB (542 words) - 11:27, 9 April 2014
- ...d store the results in memory. Afterwards he can decrypt the ciphertext by computing ''D<sub>K</sub>''(''C'') for each ''K''. Any matches between these two resu ...3 KB (474 words) - 09:45, 20 October 2014
- |data17 = '''Probability and Computing''' (2E) <br> Michael Mitzenmacher and Eli Upfal <br> Cambridge University * '''[MU]''' ''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis ...15 KB (1,465 words) - 13:36, 30 April 2024
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...9 KB (1,662 words) - 07:05, 15 November 2011
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...3 KB (604 words) - 09:12, 23 November 2015
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...3 KB (604 words) - 05:32, 31 October 2016
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...3 KB (622 words) - 11:08, 22 December 2020
- ...mal language] (not entirely the same thing as the c language). The task of computing <math>f(x)</math> is equivalent to that of determining whether <math>x\in L ...nomial size certificate, the algorithm <math>A</math> verifies (instead of computing) the <math>f(x)</math> for any positive instance <math>x</math> in polynomi ...11 KB (1,828 words) - 06:00, 27 August 2011
- A naive way of checking the equality is first computing <math>AB</math> and then comparing the result with <math>C</math>. The (asy ...4 KB (694 words) - 03:25, 23 July 2011
- ;The Monte Carlo method for computing <math>\mathrm{e}</math> ...4 KB (606 words) - 01:47, 10 October 2011
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...3 KB (666 words) - 04:44, 23 July 2013
- * [[Computer language]] for application of formal languages in computing ...5 KB (710 words) - 00:57, 25 February 2017
- ...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...5 KB (881 words) - 02:35, 19 July 2011
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...4 KB (762 words) - 08:28, 19 November 2019
- ...r <math>v</math> is adjacent to a vertex in <math>D</math>. The problem of computing minimum dominating set is NP-hard. ...4 KB (769 words) - 12:19, 12 November 2017
- ...ok.html|title = Proceedings of the Third Annual ACM Symposium on Theory of Computing|pages = 151–158}}</ref> ...ust 1% of the worst-case number of computation and that saves a ''lot'' of computing, but that is still <math>0.01 \times (2^n)</math> computations. And every e ...15 KB (2,427 words) - 22:24, 16 August 2017
- |data17 = '''Probability and Computing''' (2E) <br> Michael Mitzenmacher and Eli Upfal <br> Cambridge University * '''[MU]''' ''Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis ...21 KB (2,167 words) - 07:44, 27 February 2024
- Computing the moment generating function <math>\mathbf{E}[e^{\lambda X}]</math>: We propose an extremely simple "randomized algorithm" for computing a <math>b\in\{-1,+1\}^m</math>: for each <math>i=1,2,\ldots, m</math>, let ...15 KB (2,761 words) - 06:11, 8 December 2015
- ...tudies of algorithms for elimination orderings in combinatorial scientific computing, our result is the first rigorous incorporation of randomized tools in this :Huacheng Yu (俞华程) is a postdoctoral researcher in the Theory of Computing group at Harvard University. He obtained his PhD from Stanford University i ...14 KB (1,850 words) - 01:51, 7 May 2018
- We propose an extremely simple "randomized algorithm" for computing a <math>b\in\{-1,+1\}^m</math>: for each <math>i=1,2,\ldots, m</math>, let ...5 KB (952 words) - 02:52, 19 July 2011
- ...> multiplications, which is too expensive. We describe an efficient way of computing the [http://en.wikipedia.org/wiki/Modular_exponentiation modular exponent] ...ed a number instead of a list of all colorings, we expect cleverer ways of computing this number than the brute force enumeration. ...29 KB (4,994 words) - 01:21, 29 August 2011
- ...he search for new Mersenne primes is the goal of the [[GIMPS]] distributed computing project. *[http://www.oddperfect.org OddPerfect.org] A projected distributed computing project to search for odd perfect numbers. ...12 KB (1,697 words) - 23:40, 1 August 2016
- |data13 = Mitzenmacher and Upfal. <br>''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. <br> Cambridge Univ Pr ...9 KB (893 words) - 12:43, 15 September 2017
- [[Decryption]] of a ciphertext <math>(R_n, L_n)</math> is accomplished by computing for <math>i=n,n-1,\ldots,1</math> ...5 KB (757 words) - 08:22, 4 April 2017
- ...]</math> by the definition of expectations. There is also a smarter way of computing <math>\mathbf{E}[X]</math>, by using indicators and the linearity of expec ...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...26 KB (4,811 words) - 10:33, 11 March 2013
- |data13 = Mitzenmacher and Upfal. <br>''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. <br> Cambridge Univ Pr ...9 KB (846 words) - 07:34, 2 June 2014
- Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...33 KB (6,205 words) - 01:11, 22 September 2011
- Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...33 KB (6,227 words) - 07:00, 29 September 2016
- Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...33 KB (6,227 words) - 06:15, 30 September 2019
- Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...33 KB (6,227 words) - 09:51, 19 March 2024
- Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...33 KB (6,227 words) - 11:45, 15 October 2017
- Generally, the '''Principle of Inclusion-Exclusion''' states the rule for computing the union of <math>n</math> finite sets <math>A_1,A_2,\ldots,A_n</math>, su === Computing Möbius functions=== ...33 KB (6,227 words) - 12:45, 16 March 2023
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...16 KB (2,886 words) - 07:49, 13 November 2011
- ...]</math> by the definition of expectations. There is also a smarter way of computing <math>\mathbf{E}[X]</math>, by using indicators and the linearity of expec ...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...26 KB (4,614 words) - 07:53, 10 March 2014
- * '''Reading assignment''': Mitzenmacher and Upfal, ''Probability and Computing, second edition'', '''Chapter 17''' "Balanced Allocations and Cuckoo Hashin ...13 KB (1,313 words) - 05:54, 11 October 2022
- |data13 = Mitzenmacher and Upfal. <br>''Probability and Computing: Randomized Algorithms and Probabilistic Analysis''. <br> Cambridge Univ Pr ...10 KB (1,029 words) - 12:44, 15 September 2017
- ...on algorithms for counting and sampling problems. Typical problems include computing marginal probabilities and expectations of random variables, the evaluation ...16 KB (900 words) - 04:52, 13 November 2020
- ...on algorithms for counting and sampling problems. Typical problems include computing marginal probabilities and expectations of random variables, the evaluation ...16 KB (900 words) - 04:54, 13 November 2020
- == Computing graph expansion == ...can be verified in poly-time. However, there is no efficient algorithm for computing the <math>\phi(G)</math> unless '''NP'''='''P'''. ...34 KB (6,244 words) - 15:28, 8 June 2013
- ...ber of perfect matchings of <math>G</math>. This problem can be reduced to computing the '''permanent''' of a square matrix. ...his problem can be reduced to computing the permanent, thus the problem of computing the permanents is also '''#P-hard'''. ...37 KB (6,579 words) - 08:26, 7 June 2010
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,354 words) - 13:38, 18 September 2018
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,354 words) - 11:26, 8 September 2020
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,354 words) - 05:43, 13 September 2022
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,354 words) - 13:18, 6 September 2019
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,354 words) - 08:06, 6 September 2021
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,348 words) - 12:54, 17 September 2017
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...30 KB (5,347 words) - 05:55, 26 November 2016
- Computing the moment generating function <math>\mathbf{E}[e^{\lambda X}]</math>: We propose an extremely simple "randomized algorithm" for computing a <math>b\in\{-1,+1\}^m</math>: for each <math>i=1,2,\ldots, m</math>, let ...27 KB (4,865 words) - 07:47, 24 March 2014
- Computing the moment generating function <math>\mathbf{E}[e^{\lambda X}]</math>: The problem raises from parallel computing. Consider that we have <math>N</math> processors, connected by a communicat ...27 KB (4,865 words) - 08:14, 24 March 2014
- Computing the moment generating function <math>\mathbf{E}[e^{\lambda X}]</math>: ...10 KB (1,796 words) - 02:51, 19 July 2011
- == Computing graph expansion == ...can be verified in poly-time. However, there is no efficient algorithm for computing the <math>\phi(G)</math> unless '''NP'''='''P'''. ...37 KB (6,824 words) - 02:20, 29 December 2015
- We propose an extremely simple "randomized algorithm" for computing a <math>b\in\{-1,+1\}^m</math>: for each <math>i=1,2,\ldots, m</math>, let The problem raises from parallel computing. Consider that we have <math>N</math> processors, connected by a communicat ...17 KB (3,066 words) - 06:06, 18 April 2013
- ...> multiplications, which is too expensive. We describe an efficient way of computing the [http://en.wikipedia.org/wiki/Modular_exponentiation modular exponent] ...21 KB (3,794 words) - 09:47, 10 September 2015
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...20 KB (3,617 words) - 01:24, 8 June 2010
- |caption = ''Probability and Computing: Randomized Algorithms and Probabilistic Analysis'', Mitzenmacher and Upfal ...12 KB (1,037 words) - 12:45, 15 September 2017
- ...d the analysis of random graphs by [Janson, Combinatorics, Probability and Computing `94]. This leads to a routine that in quadratic time, sparsifies a graph do ...7 KB (999 words) - 05:35, 13 July 2017
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...8 KB (1,547 words) - 08:58, 16 October 2011
- == Computing graph expansion == ...can be verified in poly-time. However, there is no efficient algorithm for computing the <math>\phi(G)</math> unless '''NP'''='''P'''. ...41 KB (7,547 words) - 09:24, 22 May 2023
- ...]</math> by the definition of expectations. There is also a smarter way of computing <math>\mathbf{E}[X]</math>, by using indicators and the linearity of expec ...e need the following theorem, which holds generally and is very useful for computing the AND of many events. ...34 KB (5,979 words) - 13:52, 20 September 2010
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...10 KB (1,940 words) - 10:53, 10 October 2023
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...10 KB (1,940 words) - 22:39, 15 September 2020
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...10 KB (1,940 words) - 12:53, 11 October 2022
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...10 KB (1,940 words) - 03:37, 19 October 2021
- The proposition can be formally verified by computing these expectations. Although these equations look formal, the intuitive int ...10 KB (1,940 words) - 07:38, 14 October 2019
- *Let <math>F_C = F_A \land F_B</math> be the Bloom filter formed by computing the bitwise AND of <math>F_A</math> and <math>F_B</math>. Argue that <math> ...9 KB (1,531 words) - 10:30, 18 October 2021
- ...y | first4=BP | year=2007 | title=Numerical Recipes: The Art of Scientific Computing | edition=3rd | publisher=Cambridge University Press | publication-place=N ...8 KB (1,133 words) - 09:45, 26 June 2017
- ...mal language] (not entirely the same thing as the c language). The task of computing <math>f(x)</math> is equivalent to that of determining whether <math>x\in L ...nomial size certificate, the algorithm <math>A</math> verifies (instead of computing) the <math>f(x)</math> for any positive instance <math>x</math> in polynomi ...25 KB (4,263 words) - 08:43, 7 June 2010
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...37 KB (6,665 words) - 12:21, 19 September 2023
- ...ath>G(n,p)</math> is connected, then we can compare the probabilities, but computing the probability that a random graph is connected is a very non-trivial task ...show that with coupling, we can compare two distributions without actually computing the probabilities. ...29 KB (4,888 words) - 09:13, 16 December 2011
- ...solve problems of other areas such as [[engineering]], [[physics]], and [[computing]]. ...9 KB (1,088 words) - 18:04, 22 August 2017
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...22 KB (3,591 words) - 03:54, 17 February 2014
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...22 KB (3,591 words) - 10:45, 4 March 2013
- #* See Chapter 7.1.1 of Probability and Computing for an analysis of the random walk algorithm for 2SAT ...13 KB (1,427 words) - 15:57, 9 January 2024
- ...for deterministic communication protocols, this is the best we can get for computing EQ. :Any deterministic communication protocol computing EQ on two <math>n</math>-bit strings costs <math>n</math> bits of communica ...28 KB (5,169 words) - 11:26, 13 September 2015