Relative expressive power of downward fragments of navigational query languages on trees and chains

Pilachowski

Gucht

et al. 2020

The Computer Journal

Self Cite

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.

Section: Discussionmentioning

confidence: 99%

“…operator (transitive closure). Examples of such relation-algebrainspired query languages include XPath and its many formalizations [2,3,5,20,21,26,27], GXPath [19], the (nested) regular path queries [1], and the navigational expressions [7,8,10,12,24]. In these languages, graph navigation is primarily supported by composition (•).…”

Section: Introductionmentioning

confidence: 99%

From Relation Algebra to Semi-join Algebra: An Approach to Graph Query Optimization

Pilachowski

Gucht

et al. 2020

The Computer Journal

Self Cite

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

From relation algebra to semi-join algebra

Proceedings of the 16th International Symposium on Database Programming Languages

Pilachowski

Gucht

et al. 2017

Self Cite

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;

“…In Section 6, we generalize Proposition 30 to also include coprojections. Finally, Hellings et al [16,17] studied the relative expressiveness of the fragments of N (π, π, ∩, −), 13 and obtained the following results which are used in this study: The graph query results of Fletcher et al [10,11] include many separation results of which the proofs do not specialize to trees. They also proved a collapse result, that automatically does hold on trees:…”

Section: Related Workmentioning

confidence: 99%

The Power of Tarski’s Relation Algebra on Trees

Lecture Notes in Computer Science

Gyssens

et al. 2018

Self Cite

Fragments of Tarski's relation algebra form the basis of many versatile graph and tree query languages including the regular path queries, XPath, and SPARQL. Surprisingly, however, a systematic study of the relative expressive power of relation algebra fragments on trees has not yet been undertaken. Our approach is to start from a basic fragment which only allows composition and union. We then study how the expressive power of the query language changes if we add diversity, converse, projections, coprojections, intersections, and/or difference, both for path queries and Boolean queries. For path queries, we found that adding intersection and difference yields more expressive power for some fragments, while adding one of the other operators always yields more expressive power. For Boolean queries, we obtain a similar picture for the relative expressive power, except for a few fragments where adding converse or projection yields no more expressive power. One challenging problem remains open, however, for both path and Boolean queries: does adding difference yields more expressive power to fragments containing at least diversity, coprojections, and intersection?