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- Eyal Rozenman, Salil P. Vadhan
- Electronic Colloquium on Computational Complexity
- 2005

We introduce a “derandomized” analogue of graph squaring. This operation increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree. One application of this product is an alternative proof of… (More)

- Nathan Linial, Eyal Rozenman
- Combinatorica
- 2005

- Alon Amit, Nathan Linial, Jirí Matousek, Eyal Rozenman
- SODA
- 2001

We describe here a simple probabilistic model for graphs that are lifts of a fixed base graph <i>G</i>, i.e., those graphs from which there is a covering man onto <i>G</i>. Our aim is to investigate the properties of typical graphs in this class. In particular, we show that almost every lift of <i>G</i> is δ(<i>G</i>)-connected where δ(<i>G</i>)… (More)

- Eyal Rozenman, Aner Shalev, Avi Wigderson
- Theory of Computing
- 2006

We construct a sequence of groups Gn, and explicit sets of generators Yn ⊂ Gn, such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 is the alternating group Ad, the set of even permutations on the elements {1, 2, . . . , d}. The group Gn is the group of all even symmetries of the rooted d-regular… (More)

- Eyal Rozenman, Aner Shalev, Avi Wigderson
- STOC
- 2004

We assume that for some <i>fixed</i> large enough integer d, the symmetric group S<inf>d</inf> can be generated as an expander using d<sup>1/30</sup> generators. Under this assumption, we explicitly construct an infinite family of groups G<inf>n</inf>, and explicit sets of generators Y<inf>n</inf> ⊂ G<inf>n</inf>, such that all generating sets have… (More)

- Nathan Linial, Eyal Rozenman
- Graphs and Combinatorics
- 2002

Let G 1⁄4 ðIn;EÞ be the graph of the n-dimensional cube. Namely, In 1⁄4 f0; 1g and 1⁄2x; y 2 E whenever jjx yjj1 1⁄4 1. For A In and x 2 A define hAðxÞ 1⁄4 #fy 2 In n Aj1⁄2x; y 2 Eg, i.e., the number of vertices adjacent to x outside of A. Talagrand, followingMargulis, proves that for every set A In of size 2n 1 we have 1 2n P x2A… (More)

- Salil P. Vadhan, Luca Trevisan, +59 authors Greg Price
- 2012

This is a survey of pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number… (More)

- Salil P. Vadhan, Luca Trevisan, +61 authors Shrenik Shah
- 2011

Pseudorandomness is the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. This survey of the subject places particular emphasis on the intimate connections that have been discovered between a variety of fundamental “pseudorandom objects” that at first seem very different in nature: expander… (More)

- Salil P. Vadhan, Luca Trevisan, +52 authors Neal Wadhwa
- 2009

This is the second volume of a 2-part survey on pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness. The survey places particular emphasis on the intimate connections that have been discovered between a variety of fundamental “pseudorandom objects” that at first seem very… (More)