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.
翻译:对于每个固定的 $ d $ $\ mathbb{N} $,我们设计一个数据结构,它代表一个二进制 $n\ times n$ 矩阵,由 $- $- twin 顺序排列。数据结构占用了 $_ d(n) 位元,这是人们最不希望得到的,并且可以对每个查询的输入及时查询$O_ d(\log\log n) 。