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REPORTS > KEYWORD > SPECTRAL GRAPH THEORY:
Reports tagged with spectral graph theory:
TR05-092 | 23rd August 2005

#### Derandomized Squaring of Graphs

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 ... more >>>

TR13-114 | 24th August 2013
Parikshit Gopalan, Salil Vadhan, Yuan Zhou

#### Locally Testable Codes and Cayley Graphs

Revisions: 1

We give two new characterizations of ($\F_2$-linear) locally testable error-correcting codes in terms of Cayley graphs over $\F_2^h$:

\begin{enumerate}
\item A locally testable code is equivalent to a Cayley graph over $\F_2^h$ whose set of generators is significantly larger than $h$ and has no short linear dependencies, but yields a ... more >>>

TR20-170 | 9th November 2020
Max Hopkins, Tali Kaufman, Shachar Lovett

#### High Dimensional Expanders: Random Walks, Pseudorandomness, and Unique Games

Revisions: 1

Higher order random walks (HD-walks) on high dimensional expanders have played a crucial role in a number of recent breakthroughs in theoretical computer science, perhaps most famously in the recent resolution of the Mihail-Vazirani conjecture (Anari et al. STOC 2019), which focuses on HD-walks on one-sided local-spectral expanders. In this ... more >>>

TR21-019 | 17th February 2021

#### Pseudodistributions That Beat All Pseudorandom Generators

Revisions: 1

A recent paper of Braverman, Cohen, and Garg (STOC 2018) introduced the concept of a pseudorandom pseudodistribution generator (PRPG), which amounts to a pseudorandom generator (PRG) whose outputs are accompanied with real coefficients that scale the acceptance probabilities of any potential distinguisher. They gave an explicit construction of PRPGs for ... more >>>

TR21-108 | 22nd July 2021
The classic Impagliazzo--Nisan--Wigderson (INW) psesudorandom generator (PRG) (STOC `94) for space-bounded computation uses a seed of length $O(\log n \cdot \log(nwd/\varepsilon))$ to fool ordered branching programs of length $n$, width $w$, and alphabet size $d$ to within error $\varepsilon$. A series of works have shown that the analysis of the ... more >>>