[Paper Review] Tractable vs. Intractable Cases of Matching Dependencies for Query Answering under Entity Resolution

Leopoldo Bertossi, Jaffer Gardezi|arXiv (Cornell University)|Sep 7, 2013

Data Quality and Management21 references3 citations

TL;DR

This paper investigates the complexity of query answering under matching dependencies (MDs) in entity resolution, focusing on acyclic MD sets. It establishes a dichotomy between tractable and NP-hard cases for resolved query answering, showing that certain syntactic conditions on pairs of MDs determine intractability, while their absence ensures tractability under transitive similarity—offering the first such dichotomy result in this context.

ABSTRACT

Matching Dependencies (MDs) are a relatively recent proposal for declarative entity resolution. They are rules that specify, on the basis of similarities satisfied by values in a database, what values should be considered duplicates, and have to be matched. On the basis of a chase-like procedure for MD enforcement, we can obtain clean (duplicate-free) instances; actually possibly several of them. The resolved answers to queries are those that are invariant under the resulting class of resolved instances. Previous work identified certain classes of queries and sets of MDs for which resolved query answering is tractable. Special emphasis was placed on cyclic sets of MDs. In this work we further investigate the complexity of this problem, identifying intractable cases, and exploring the frontier between tractability and intractability. We concentrate mostly on acyclic sets of MDs. For a special case we obtain a dichotomy result relative to NP-hardness.

Motivation & Objective

• To systematically analyze the complexity of resolved query answering under matching dependencies (MDs), especially for acyclic MD sets.
• To identify syntactic criteria on pairs of MDs that lead to NP-hardness in resolved query answering.
• To establish a dichotomy between tractable and intractable cases for acyclic MDs under transitive similarity operators.
• To extend the dichotomy result beyond pairs of MDs to larger sets, complementing prior work on cyclic MDs.
• To clarify the frontier between tractability and intractability in MD-based entity resolution, particularly contrasting acyclic and cyclic dependencies.

Proposed method

• The authors define a chase-based semantics for cleaning databases by enforcing MDs, generating clean (duplicate-free) instances.
• They formalize resolved query answering as the set of answers that are invariant across all minimal clean instances derived from the chase.
• They introduce syntactic conditions on pairs of MDs that, when satisfied, imply NP-hardness of the query answering problem.
• They prove that when these conditions are absent and similarity is transitive, the problem becomes tractable, leading to a dichotomy.
• They extend the analysis to sets of more than two MDs, maintaining the dichotomy under acyclic dependency structures.
• They compare their semantics with alternative chase-based approaches and discuss implications for query rewriting and repair semantics.

Experimental results

Research questions

• RQ1 What syntactic properties of acyclic matching dependency pairs lead to NP-hardness in resolved query answering?
• RQ2 Can a dichotomy between tractable and intractable cases be established for acyclic MDs under transitive similarity?
• RQ3 How does the presence of cycles in MD sets compare to acyclic sets in terms of complexity of resolved query answering?
• RQ4 To what extent do alternative chase semantics (e.g., one-MD-at-a-time) alter the complexity landscape of resolved query answering?
• RQ5 Can the dichotomy result be extended to larger sets of acyclic MDs beyond pairs?

Key findings

• For acyclic sets of MDs, the presence of specific syntactic patterns in pairs of MDs leads to NP-hardness in resolved query answering.
• When these intractable patterns are absent and similarity is transitive, resolved query answering becomes tractable, establishing a dichotomy for linear pairs of MDs.
• The dichotomy result holds under the assumption of transitive similarity operators, which is crucial for the tractability proof.
• In contrast to prior work on cyclic MDs (e.g., HSC sets), which are tractable, acyclic MDs can still lead to intractable query answering, challenging the intuition that cycles simplify the problem.
• The results are complementary to prior work on cyclic MDs, providing a broader complexity landscape for MD-based entity resolution.
• Alternative chase semantics that process MDs one at a time can make previously intractable cases tractable, highlighting the sensitivity of complexity to semantics design.