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- W4300659301 abstract "We consider a problem which has received considerable attention in systems literature because of its applications to routing in delay tolerant networks and replica placement in distributed storage systems. In abstract terms the problem can be stated as follows: Given a random variable $X$ generated by a known product distribution over ${0,1}^n$ and a target value $0 leq theta leq 1$, output a non-negative vector $w$, with $|w|_1 le 1$, which maximizes the probability of the event $w cdot X ge theta$. This is a challenging non-convex optimization problem for which even computing the value $Pr[w cdot X ge theta]$ of a proposed solution vector $w$ is #P-hard. We provide an additive EPTAS for this problem which, for constant-bounded product distributions, runs in $ poly(n) cdot 2^{poly(1/eps)}$ time and outputs an $eps$-approximately optimal solution vector $w$ for this problem. Our approach is inspired by, and extends, recent structural results from the complexity-theoretic study of linear threshold functions. Furthermore, in spite of the objective function being non-smooth, we give a emph{unicriterion} PTAS while previous work for such objective functions has typically led to a emph{bicriterion} PTAS. We believe our techniques may be applicable to get unicriterion PTAS for other non-smooth objective functions." @default.
- W4300659301 created "2022-10-03" @default.
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- W4300659301 date "2013-07-13" @default.
- W4300659301 modified "2023-09-29" @default.
- W4300659301 title "A Polynomial-time Approximation Scheme for Fault-tolerant Distributed Storage" @default.
- W4300659301 doi "https://doi.org/10.48550/arxiv.1307.3621" @default.
- W4300659301 hasPublicationYear "2013" @default.
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