绘制某些合取查询查询的可处理性边界
Charting the Tractability Frontier of Certain Conjunctive Query Answering
摘要：
不确定数据库定义为不需要满足主键的关系数据库。这样的数据库的修复（或可能世界）通过选择最大数量的元组而不选择具有相同主键码值的两个不同元组来获得。对于布尔查询q，决策问题CERTAINTY（q）将不确定数据库db作为输入，并询问db的每次修复是否满足q。我们的主要重点是非循环布尔合取查询没有自我加入。以前的工作已经引入了这种查询的（有向）攻击图的概念，并证明了CERTAINTY（q）是一阶可表达的当且仅当q的攻击图是非循环的。本文研究了确定性（q）的易处理性和难处理性之间的界限。我们首先将攻击图中的循环分类为弱或强，然后证明以下内容。如果一个查询q的攻击图包含一个强循环，则CERTAINTY（q）是coNP完全的。如果q的攻击图不包含强圈且其每个弱圈都是终端的（即，没有边从圈中的顶点通向圈外的顶点），则CERTAINTY（q）在P中。然后我们部分地解决唯一剩余的开放情况，即，当攻击图中存在非终结环且不存在强环时，最后，我们在概率数据库上建立了CERTAINTY（q）的复杂性和评估q之间的关系。
英文摘要：
An uncertain database is defined as a relational database in which primary keys need not be satisfied. A repair (or possible world) of such database is obtained by selecting a maximal number of tuples without ever selecting two distinct tuples with the same primary key value. For a Boolean query q, the decision problem CERTAINTY(q) takes as input an uncertain database db and asks whether q is satisfied by every repair of db. Our main focus is on acyclic Boolean conjunctive queries without self-join. Previous work has introduced the notion of (directed) attack graph of such queries, and has proved that CERTAINTY(q) is first-order expressible if and only if the attack graph of q is acyclic. The current paper investigates the boundary between tractability and intractability of CERTAINTY(q). We first classify cycles in attack graphs as either weak or strong, and then prove among others the following. If the attack graph of a query q contains a strong cycle, then CERTAINTY(q) is coNP-complete. If the attack graph of q contains no strong cycle and every weak cycle of it is terminal (i.e., no edge leads from a vertex in the cycle to a vertex outside the cycle), then CERTAINTY(q) is in P. We then partially address the only remaining open case, i.e., when the attack graph contains some nonterminal cycle and no strong cycle. Finally, we establish a relationship between the complexities of CERTAINTY(q) and evaluating q on probabilistic databases.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
