A polynomial-time approximation scheme for fault-tolerant distributed storage

Constantinos Daskalakis, Anindya De, Ilias Diakonikolas, Ankur Moitra, Rocco A. Servedio

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

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 χ generated by a known product distribution over {0,1}n and a target value 0 ≤ θ ≤ 1, output a non-negative vector ω, with ||ω||1 ≤ 1, which maximizes the probability of the event ω χ ≥ θ. This is a challenging non-convex optimization problem for which even computing the value Pr[w·X > θ] 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) · 2Poly(1/ε) time and outputs an ε-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 func-tions. Furthermore, in spite of the objective function being non-smooth, we give a unicriterion PTAS while previous work for such objective functions has typically led to a bicriterion PTAS. We believe our techniques may be applicable to get unicriterion PTAS for other non-smooth objective functions.

Original languageEnglish (US)
Title of host publicationProceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
PublisherAssociation for Computing Machinery
Pages628-644
Number of pages17
ISBN (Print)9781611973389
DOIs
StatePublished - 2014
Event25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014 - Portland, OR, United States
Duration: Jan 5 2014Jan 7 2014

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014
CountryUnited States
CityPortland, OR
Period1/5/141/7/14

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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