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.

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Many graph query languages rely on the composition operator to navigate graphs and select nodes of interests, even though evaluating compositions of relations can be costly. Often, this need for composition can be reduced by rewriting towards queries that use semi-joins instead. In this way, the cost of evaluating queries can be signi cantly reduced. We study techniques to recognize and apply such rewritings. Concretely, we study the relationship between the expressive power of the relation algebras, that heavily rely on composition, and the semi-join algebras, that replace the composition operator in favor of the semi-join operators. As our main result, we show that each fragment of the relation algebras where intersection and/or di erence 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 that evaluate to sets of nodes. For practical relevance, we exhibit constructive steps for rewriting relation algebra queries to semi-join algebra queries, and prove that these steps lead to only a well-bounded increase in the number of steps needed to evaluate the rewritten queries. In addition, on node-labeled graphs that are 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 xpoint operators. CCS CONCEPTS • Theory of computation → Database query processing and optimization (theory); Logic and databases; Database query languages (principles); Finite Model Theory;

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