Kevin Pratt

collaborators

4 papers

cs.DS2026

An algorithm for $k$ -set cover

Josh Alman, Baitian Li, Kevin Pratt

We show that set cover on a universe of size $n$ and with sets of size at most $k$ can be solved in time $2^{(1 - 1/ k + O (1/ k^{3/2})) n}$ . This improves on a $2^{(1 - 0.929/ k) n}$ -time alg…

cs.DS2026

Breaking the $2^{n}$ barrier for graph $k$ -coloring

Kevin Pratt

We show that for all $k$ , there exists $ε_{k} > 0$ such that graph $k$ -coloring can be solved by a randomized algorithm with one-sided error in time $O((2-\varepsilon_k)^n)…

cs.CC2026

The edge of the asymptotic spectrum of tensors

Josh Alman, Baitian Li, Kevin Pratt

Strassen founded the theory of the asymptotic spectrum of tensors to study the complexity of matrix multiplication. A central challenge in this theory is to explicitly construct ne…

cs.DS2025

Faster Convolutions: Yates and Strassen Revisited

Cornelius Brand, Radu Curticapean, Baitian Li +1

Given two vectors $u, v \in Q^{D}$ over a finite domain $D$ and a function $f : D \times D \to D$ , the convolution problem asks to compute the vector $w \in Q^{D}$ whose…

An algorithm for k-set cover

Breaking the 2n barrier for graph k-coloring

The edge of the asymptotic spectrum of tensors

Faster Convolutions: Yates and Strassen Revisited

An algorithm for $k$ -set cover

Breaking the $2^{n}$ barrier for graph $k$ -coloring