Covers in hypergraphs are frequently studied to capture various forms of dependence between hyperedges. For example, even covers--which check if each vertex appears in an even number of hyperedges--have found much success recently in the study of locally decodable codes. Inspired by a recently-emerging line of work on...
Joshua Brakensiek, V. Guruswami, Aaron L. Putterman· 1 citation
We study the one-pass streaming complexity of CSPs over a fixed finite relation $R$ under three natural objectives: $\textsf{SAT}(R)$, deciding whether all constraints can be satisfied; $\textsf{Min}$-$\textsf{CSP}(R)$, approximately minimizing the number of unsatisfied constraints; and $\textsf{Exact-CSP}(R)$, exactly...
Joshua Brakensiek, Aaron L. Putterman, Amatya Sharma et al.· 0 citations
We extend the recent work of Reis and Rothvoss on sparsifying sums of $\ell_1$ norms to the more general task of sparsifying (Minkowski) sums of centrally symmetric, convex sets. As our main result, we prove that for any $\varepsilon>0$ and centrally symmetric, convex sets $C_1, \ldots, C_m\subseteq\mathbb{R}^n$ there...
Arpon Basu, Joshua Brakensiek, Ye-Yuan Chen et al.· 0 citations
This work begins a systematic study of basic problems in directed \emph{acyclic} graphs (DAGs) and shows that reachability from a single vertex and even topological sorting are both computable in O(n \log^3 n) many cut queries.
