Many graph query languages rely on composition to navigate graphs and select nodes of interest, even though evaluating compositions of relations can be costly. Often, this need for composition can be reduced by rewriting toward queries using semi-joins instead, resulting in a significant reduction of the query evaluation cost. We study techniques to recognize and apply such rewritings. Concretely, we study the relationship between the expressive power of the relation algebras, which heavily rely on composition, and the semi-join algebras, which replace composition in favor of semi-joins. Our main result is that each fragment of the relation algebras where intersection and/or difference is only used on edges (and not on complex compositions) is expressively equivalent to a fragment of the semi-join algebras. This expressive equivalence holds for node queries evaluating to sets of nodes. For practical relevance, we exhibit constructive rules for rewriting relation algebra queries to semi-join algebra queries and prove that they lead to only a well-bounded increase in the number of steps needed to evaluate the rewritten queries. In addition, on sibling-ordered trees, we establish new relationships among the expressive power of Regular XPath, Conditional XPath, FO-logic and the semi-join algebra augmented with restricted fixpoint operators.

中文翻译：

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从关系代数到半联接代数：一种图查询优化方法

许多图形查询语言都依赖于组合来导航图形并选择感兴趣的节点，即使评估关系的组合可能会很昂贵。通常，可以通过改为使用半联接重写查询来减少这种组合需求，从而大大降低了查询评估成本。我们研究识别和应用此类重写的技术。具体来说，我们研究关系代数的表达能力（主要依赖于合成）和半联接代数（代替联接以有利于半联接）的表达能力之间的关系。我们的主要结果是，关系代数的每个片段（仅在边上（而不是在复杂的成分上）使用交集和/或差）在表达上等效于半联接代数的片段。这种表达等效性适用于评估节点集的节点查询。对于实际的相关性，我们展示了用于将关系代数查询重写为半联接代数查询的建设性规则，并证明它们仅导致评估重写查询所需的步骤数量有很大的增加。此外，在同级有序树上，我们在规则XPath，条件XPath，FO-logic和受限约束点运算符扩充的半联接代数的表达能力之间建立新的关系。