An improved algorithm for learning sparse parities in the presence of noise

Yan, Di; Yu, Yu; Liu, Hanlin; Zhao, Shuoyao; Zhang, Jiang

doi:10.1016/j.tcs.2021.04.026

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Book1

Other1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When the number of relevant variables 1 k of the parity function f is known (f is called k-sparse parity), all the algorithms proposed in the literature run in time n ck for some constant c < 1, [5,7,22,33,36]. Finding a polynomial-time algorithm for k-sparse parities for some k = ω(1), or proving the impossibility of such an algorithm, is another significant and unresolved challenge.…”

Section: Introductionmentioning

confidence: 99%

Bounds for the Number of Tests in Non-adaptive Randomized Algorithms for Group Testing

Bshouty

Haddad

Haddad-Zaknoon

2020

SOFSEM 2020: Theory and Practice of Computer Science

View full text Add to dashboard Cite

We study the group testing problem with non-adaptive randomized algorithms. Several models have been discussed in the literature to determine how to randomly choose the tests. For a model M, let mM(n, d) be the minimum number of tests required to detect at most d defectives within n items, with success probability at least 1 − δ, for some constant δ. In this paper, we study the measures cM(d) = lim n→∞ mM(n, d) ln n and cM = lim d→∞ cM(d) d .In the literature, the analyses of such models only give upper bounds for cM(d) and cM, and for some of them, the bounds are not tight. We give new analyses that yield tight bounds for cM(d) and cM for all the known models M.

show abstract