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On the feasibility of semantic query metrics

George Fletcher, Peter Wood, Nikolay Yakovets

TL;DR

This work tackles the problem of defining semantic distances between relational queries by anchoring distances to containment-based paths. It first proves that no meaningful semantic metric exists for the general CQ class due to non-finiteness of maximal containment, then proposes a nontrivial restriction to 2CQs in which a well-defined, metric containment-based distance can be defined and computed. The authors show that maximal containment for 2CQs is decidable in polynomial time and provide a graph-based framework (MC-graph) to compute distances, albeit with exponential-time complexity in certain parameters. The result offers a principled, semantics-driven approach to measuring query similarity within a practically relevant fragment, enabling potential applications in workload analysis and query optimization, and sets the stage for further algorithmic and empirical investigations, including extensions to constraints.

Abstract

We consider the problem of defining semantic metrics for relational database queries. Informally, a semantic query metric for a query language $L$ is a metric function $δ:L\times L\to \mathbb{N}$ where $δ(Q_1, Q_2)$ represents the length of a shortest path between queries $Q_1$ and $Q_2$ in a graph. In this graph, nodes are queries from $L$, and edges connect semantically distinct queries where one query is maximally semantically contained in the other. Since query containment is undecidable for first-order queries, we focus on the simpler language of conjunctive queries. We establish that defining a semantic query metric is impossible even for conjunctive queries. Given this impossibility result, we identify a significant subclass of conjunctive queries where such a metric is feasible, and we establish the computational complexity of calculating distances within this language.

On the feasibility of semantic query metrics

TL;DR

This work tackles the problem of defining semantic distances between relational queries by anchoring distances to containment-based paths. It first proves that no meaningful semantic metric exists for the general CQ class due to non-finiteness of maximal containment, then proposes a nontrivial restriction to 2CQs in which a well-defined, metric containment-based distance can be defined and computed. The authors show that maximal containment for 2CQs is decidable in polynomial time and provide a graph-based framework (MC-graph) to compute distances, albeit with exponential-time complexity in certain parameters. The result offers a principled, semantics-driven approach to measuring query similarity within a practically relevant fragment, enabling potential applications in workload analysis and query optimization, and sets the stage for further algorithmic and empirical investigations, including extensions to constraints.

Abstract

We consider the problem of defining semantic metrics for relational database queries. Informally, a semantic query metric for a query language is a metric function where represents the length of a shortest path between queries and in a graph. In this graph, nodes are queries from , and edges connect semantically distinct queries where one query is maximally semantically contained in the other. Since query containment is undecidable for first-order queries, we focus on the simpler language of conjunctive queries. We establish that defining a semantic query metric is impossible even for conjunctive queries. Given this impossibility result, we identify a significant subclass of conjunctive queries where such a metric is feasible, and we establish the computational complexity of calculating distances within this language.

Paper Structure

This paper contains 13 sections, 10 theorems, 20 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Preliminary definitions
  4. Maximal query containment
  5. Non-existence results
  6. Maximal containment of 2CQs
  7. 2CQs and their restrictions
  8. Complexity of maximal containment
  9. A semantic metric for 2CQs
  10. Well-defined and well-behaved containment-based distance
  11. Complexity of computing semantic distance
  12. Related Work
  13. Discussion and next steps

Key Result

Proposition 2.4

$Q_1 \mathrel{\sqsubseteq} Q_2$ if and only if $Q_2 \to Q_1$.

Figures (3)

  • Figure 1: Equivalences among oriented path queries.
  • Figure 2: Oriented path queries $O_{111}$, $O_{11011}$ and $O_{11}$.
  • Figure 3: Oriented path query $Q_i = O_{11(01)^i1}$.

Theorems & Definitions (28)

  • Example 2.1
  • Definition 2.2
  • Definition 2.3
  • Proposition 2.4: ChandraM77
  • Example 2.5
  • Proposition 2.6: ChandraM77HellN92
  • Definition 2.7
  • Definition 3.1
  • Theorem 3.2
  • proof
  • ...and 18 more