Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with High-Dimensional Expander:
TR21-099 | 4th July 2021
Louis Golowich

Improved Product-Based High-Dimensional Expanders

High-dimensional expanders generalize the notion of expander graphs to higher-dimensional simplicial complexes. In contrast to expander graphs, only a handful of high-dimensional expander constructions have been proposed, and no elementary combinatorial construction with near-optimal expansion is known. In this paper, we introduce an improved combinatorial high-dimensional expander construction, by modifying ... more >>>

TR23-043 | 9th April 2023
Yotam Dikstein, Irit Dinur

Coboundary and cosystolic expansion without dependence on dimension or degree

We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building of $SL_n(F_q)$. The improvement applies to the high dimensional expanders constructed by Lubotzky, Samuels and Vishne, and ... more >>>

TR23-065 | 4th May 2023
Louis Golowich

From Grassmannian to Simplicial High-Dimensional Expanders

In this paper, we present a new construction of simplicial complexes of subpolynomial degree with arbitrarily good local spectral expansion. Previously, the only known high-dimensional expanders (HDXs) with arbitrarily good expansion and less than polynomial degree were based on one of two constructions, namely Ramanujan complexes and coset complexes. ... more >>>

ISSN 1433-8092 | Imprint