We present an index structure, called the color-index, to boost the evaluation of acyclic conjunctive queries (ACQs) over binary schemas. The color-index is based on the color refinement algorithm, a widely used subroutine for graph isomorphism testing algorithms. Given a database $D$, we use a suitable version of the color refinement algorithm to produce a stable coloring of $D$, an assignment from the active domain of $D$ to a set of colors $C_D$. The main ingredient of the color-index is a particular database $D_c$ whose active domain is $C_D$ and whose size is at most $|D|$. Using the color-index, we can evaluate any free-connex ACQ $Q$ over $D$ with preprocessing time $O(|Q| \cdot |D_c|)$ and constant delay enumeration. Furthermore, we can also count the number of results of $Q$ over $D$ in time $O(|Q| \cdot |D_c|)$. Given that $|D_c|$ could be much smaller than $|D|$ (even constant-size for some families of databases), the color-index is the first index structure for evaluating free-connex ACQs that allows efficient enumeration and counting with performance that may be strictly smaller than the database size.

翻译：本文提出一种名为颜色索引的索引结构，用于提升二元模式上无环连接查询的评估效率。颜色索引基于颜色细化算法——一种广泛应用于图同构测试算法的子程序。给定数据库$D$，我们采用颜色细化算法的适配版本生成$D$的稳定着色，即将$D$的有效域映射到颜色集合$C_D$的赋值方案。颜色索引的核心构件是一个特殊数据库$D_c$，其有效域为$C_D$且规模不超过$|D|$。通过颜色索引，我们能够以$O(|Q| \cdot |D_c|)$的预处理时间和常数延迟枚举，评估数据库$D$上任意自由连接无环查询$Q$。此外，我们还可在$O(|Q| \cdot |D_c|)$时间内计算$Q$在$D$上的结果数量。鉴于$|D_c|$可能远小于$|D|$（对某些数据库族甚至保持恒定规模），颜色索引成为首个支持高效枚举与计数的自由连接无环查询索引结构，其性能指标可严格低于数据库规模。