@inbook{b8cb39709b8b45c79fdb5fdfccb88abd,
title = "Deconstructing 1-local expanders",
abstract = "A 1-local 2d-regular 2n-vertex graph is represented by d bijections over {0,1}n such that each bit in the output of each bijection is a function of a single bit in the input. An explicit construction of 1-local expanders was presented by Viola and Wigderson (ECCC, TR16-129, 2016), and the goal of the current work is to de-construct it; that is, make its underlying ideas more transparent. Starting from a generic candidate for a 1-local expander (over {0,1}n), we first observe that its underlying bijections consists of pairs of (“relocation”) permutations over [n] and offsets (which are n-bit long strings). Next, we formulate a natural problem regarding “coordinated random walks” (CRW) on the corresponding (n-vertex) “relocation” graph, and prove the following two facts: 1.Any solution to the CRW problem yields 1-local expanders.2.Any constant-size expanding set of generators for the symmetric group (over [n]) yields a solution to the CRW problem. This yields an alternative construction and different analysis than the one used by Viola and Wigderson. Furthermore, we show that solving (a relaxed version of) the CRW problem is equivalent to constructing 1-local expanders.",
author = "Oded Goldreich",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.",
year = "2020",
month = apr,
day = "4",
doi = "10.1007/978-3-030-43662-9_14",
language = "الإنجليزيّة",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "220--248",
editor = "Oded Goldreich",
booktitle = "Computational Complexity and Property Testing",
address = "ألمانيا",
}