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Electronic Colloquium on Computational Complexity

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Reports tagged with spectral graph theory:
TR05-092 | 23rd August 2005
Eyal Rozenman, Salil Vadhan

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 $\F_2^h$:

\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

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 >>>

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