发表机构
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出符号分数超树宽度度量，并设计变量消元算法，实现带否定合取查询的常数延迟枚举，推广了符号无环性。
AI 中文摘要
我们研究了带否定的合取查询（$\texttt{CQ}^{\neg}$）的常数延迟枚举问题。先前的工作定义了符号无环性，它刻画了可实现线性预处理时间的查询类别，但对此之外的情况知之甚少。我们为$\texttt{CQ}^{\neg}$引入了一种新的超图宽度度量——符号分数超树宽度（$\textsf{sfhw}$），其定义要求单个变量序同时处理每个负原子的子集。我们证明$\textsf{sfhw}$严格推广了符号无环性（当$\textsf{sfhw}=1$时恢复）和分数超树宽度（在无否定查询上恢复）。我们的主要算法结果是一个变量消元算法，对于任何完整的$\texttt{CQ}^{\neg}$查询，在输入$I$上实现常数延迟枚举，预处理时间为$O(|I|^{\textsf{sfhw}})$。我们进一步表明，使用多个变量序可以改进此界限，展示了对于至少有一条负边的$k$-环查询的$O(|I|^{3/2})$算法。
英文摘要
We study constant-delay enumeration for conjunctive queries with negation ($\texttt{CQ}^{\neg}$). Prior work defined \emph{signed-acyclicity}, which characterizes the class of queries where linear preprocessing time is achievable, but little has been known beyond this. We introduce a new hypergraph width measure for $\texttt{CQ}^{\neg}$, the \emph{signed fractional hypertree width} ($\textsf{sfhw}$), defined by requiring that a single variable order simultaneously handle every subset of the negative atoms. We show that $\textsf{sfhw}$ strictly generalizes signed-acyclicity (recovered when $\textsf{sfhw} = 1$) and fractional hypertree width (recovered on queries without negation). Our main algorithmic result is a variable-elimination algorithm that achieves constant-delay enumeration on input $I$ for any full $\texttt{CQ}^{\neg}$ query with preprocessing time $O(|I|^{\textsf{sfhw}})$. We further show that using multiple variable orders can improve this bound, exhibiting an $O(|I|^{3/2})$ algorithm for $k$-cycle queries with at least one negative edge.
