The tractability frontier of well-designed SPARQL queries

TL;DR

This paper characterizes the classes of well-designed SPARQL queries that can be evaluated efficiently in polynomial time, introducing a new width measure called domination width related to treewidth.

Contribution

It provides a structural characterization of polynomial-time evaluable well-designed SPARQL queries using the novel domination width measure.

Findings

Classes with bounded domination width are evaluable in polynomial time.

Unbounded domination width classes are likely intractable under certain complexity assumptions.

Introduces a new width measure linking query structure to evaluation complexity.

Abstract

We study the complexity of query evaluation of SPARQL queries. We focus on the fundamental fragment of well-designed SPARQL restricted to the AND, OPTIONAL and UNION operators. Our main result is a structural characterisation of the classes of well-designed queries that can be evaluated in polynomial time. In particular, we introduce a new notion of width called domination width, which relies on the well-known notion of treewidth. We show that, under some complexity theoretic assumptions, the classes of well-designed queries that can be evaluated in polynomial time are precisely those of bounded domination width.