A fully polynomial-time approximation scheme for approximating a sum of random variables

Given n independent integer-valued random variables X1,X2,…,Xn and an integer C, we study the fundamental problem of computing the probability that the sum X=X1+X2+⋯+Xn is at most C. We assume that each random variable Xi is implicitly given by an oracle Oi, which given two input integers n1,n2 retu...

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Vydáno v:Operations research letters Ročník 42; číslo 3; s. 197 - 202
Hlavní autoři: Li, Jian, Shi, Tianlin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.05.2014
Témata:
Algorithms
Approximate counting
Approximation
Counting
Counting knapsack
Estimates
FPTAS
Integers
Mathematical analysis
Operations research
Random variables
Tail probability
Threshold probability
Counting knapsack
Threshold probability
Tail probability
FPTAS
Approximate counting
ISSN:0167-6377, 1872-7468
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Shrnutí:Given n independent integer-valued random variables X1,X2,…,Xn and an integer C, we study the fundamental problem of computing the probability that the sum X=X1+X2+⋯+Xn is at most C. We assume that each random variable Xi is implicitly given by an oracle Oi, which given two input integers n1,n2 returns the probability of n1≤Xi≤n2. We give the first deterministic fully polynomial-time approximation scheme (FPTAS) to estimate the probability up to a relative error of 1±ϵ. Our algorithm is based on the technique for approximately counting knapsack solutions, developed in Gopalan et al. (2011).
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ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2014.02.004