2026-07-20T07:17:24Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15535 2024-03-06T10:55:32Z ddc:004 open_access

Near-Optimal Cayley Expanders for Abelian Groups Jalan, Akhil Moshkovitz, Dana Cayley graphs Expander walks Epsilon-biased sets Derandomization We give an efficient deterministic algorithm that outputs an expanding generating set for any finite abelian group. The size of the generating set is close to the randomized construction of Alon and Roichman [Alon and Roichman, 1994], improving upon various deterministic constructions in both the dependence on the dimension and the spectral gap. By obtaining optimal dependence on the dimension we resolve a conjecture of Azar, Motwani, and Naor [Azar et al., 1998] in the affirmative. Our technique is an extension of the bias amplification technique of Ta-Shma [Ta-Shma, 2017], who used random walks on expanders to obtain expanding generating sets over the additive group of 𝔽₂ⁿ. As a consequence, we obtain (i) randomness-efficient constructions of almost k-wise independent variables, (ii) a faster deterministic algorithm for the Remote Point Problem, (iii) randomness-efficient low-degree tests, and (iv) randomness-efficient verification of matrix multiplication. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Akhil Jalan and Dana Moshkovitz 2021 Is Part Of LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2021.24 urn:nbn:de:0030-drops-155359 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.24 eng https://creativecommons.org/licenses/by/4.0/legalcode