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Karp-Luby (KL) sampling [1, 2] is a Monte Carlo algorithm that is used to estimate the number of truth assignments to a set of literals x = {x1, …, xk} that satisfy a logical expression L[x] having “disjunctive normal form” (DNF). That is, L[x] has the form C1 ∨ C2 ∨⋯ ∨ Cm, where each clause Ci is a conjunction of the form \(C_i=y_{i_1}\wedge y_{i_2}\wedge \cdots \wedge y_{i_l}\) with i1, i2, …, il being distinct elements of {1, 2, …, k} and \(y_{i_j}=x_{i_j}\) or \(\neg x_{i_j}\) for 1 ≤ j ≤ l. A straightforward modification of the technique can be used to estimate P(L[X] = 1), where X = {X1, X2, …, Xk} is a set of mutually independent boolean random variables. This latter use of KL sampling plays a key role when querying uncertain data. Exact computation is #P-complex in the data size both for the original counting problem problem and for computation of p = P(L[X] = 1), which is why approximate methods are needed. A naive approach that simply generates n...
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References
Karp RM, Luby M. Monte-Carlo algorithms for enumeration and reliability problems. In: Proceedings of the IEEE Conference on Foundations of Computer Science; 1983. p. 56–64.
Karp RM, Luby M, Madras N. Monte-Carlo approximation algorithms for enumeration problems. J Algorithms. 1989;10(3):429–48.
Vazirani VV. Approximation algorithms. Berlin/New York: Springer; 2001.
Suciu D, Olteanu D, Ré C, Koch C. Probabilistic databases. Synthesis lectures on data management. Morgan & Claypool; 2011.
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Haas, P.J. (2018). Karp-Luby Sampling. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_80765
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_80765
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