Compact representation for matrices of bounded twin-width

Abstract

For every fixed $d\in \mathbb{N}$, we design a data structure that represents a binary $n\times n$ matrix that is $d$-twin-ordered. The data structure occupies $O_d(n)$ bits, which is the least one could hope for, and can be queried for entries of the matrix in time $O_d(\log \log n)$ per query.

24 pages, 2 figures