Run-Based Semantics for RPQs

TL;DR

This paper introduces run-based semantics for regular path queries (RPQs) that produce finite, tractable results suitable for practical graph database applications, while maintaining theoretical consistency with existing semantics.

Contribution

It proposes simple-run and binding-trail semantics for RPQs, balancing theoretical soundness with practical needs by ensuring finiteness and tractability.

Findings

Finiteness of results under new semantics is guaranteed.

Result emptiness testing remains tractable.

Supports bag semantics and efficient enumeration.

Abstract

The formalism of RPQs (regular path queries) is an important building block of most query languages for graph databases. RPQs are generally evaluated under homomorphism semantics; in particular only the endpoints of the matched walks are returned. Practical applications often need the full matched walks to compute aggregate values. In those cases, homomorphism semantics are not suitable since the number of matched walks can be infinite. Hence, graph-database engines adapt the semantics of RPQs, often neglecting theoretical red flags. For instance, the popular query language Cypher uses trail semantics, which ensures the result to be finite at the cost of making computational problems intractable. We propose a new kind of semantics for RPQs, including in particular simple-run and binding-trail semantics, as a candidate to reconcile theoretical considerations with practical aspirations. Both ensure the output to be finite in a way that is compatible with homomorphism semantics: projection on endpoints coincides with homomorphism semantics. Hence, testing the emptiness of result is tractable, and known methods readily apply. Moreover, simple-run and binding-trail semantics support bag semantics, and enumeration of the bag of results is tractable