Let $S\subseteq {\mathbb F}_2^u$ have size $n=2^\ell$, and let $h:{\mathbb F}_2^u\to {\mathbb F}_2^\ell$ be a uniformly random linear map. For
$y\in{\mathbb F}_2^\ell$, write ${load}_h(y):=|h^{-1}(y)\cap S|$, and let
$M(S,h):=\max_{y\in{\mathbb F}_2^\ell}\{load}_h(y)$ be the maximum load. Jaber, Kumar and Zuckerman (STOC 2025) proved that the expected maximum load of $h$ on $S$ is ... more >>>

We study the parallel complexity of computing the arboricity of a graph, defined as the minimum number of forests into which its edges can be partitioned.
For graphs of bounded treewidth, we present a simple dynamic programming–based parallel algorithm that constructs an optimal partition of the edges into forests.
For ... more >>>

A depth-4 algebraic circuit with top fan-in $k$ and bottom fan-in $2$ is a circuit $\Phi$ of the form $\Phi = \sum_{i=1}^k \prod_{j=1}^{m_i} Q_{ij}$, where the polynomials $Q_{ij} \in \mathbb{K}[x_1, \ldots, x_n]$ have degree at most $2$.
The class of all such circuits is denoted by $\Sigma^k \Pi \Sigma ... more >>>