[Paper Review] A SAT model to mine flexible sequences in transactional datasets

Rémi Coletta, Benjamin Négrevergne|arXiv (Cornell University)|Apr 1, 2016

Data Mining Algorithms and Applications10 references3 citations

TL;DR

This paper proposes a SAT-based formulation to mine frequent flexible sequences in transactional datasets, enabling efficient integration of user-defined constraints like gaps, spans, and must-contain conditions. By leveraging off-the-shelf SAT solvers and interactive solving, the approach supports scalable mining of closed and maximal patterns, demonstrating practical performance on real-world datasets while offering high flexibility for diverse application-specific needs.

ABSTRACT

Traditional pattern mining algorithms generally suffer from a lack of flexibility. In this paper, we propose a SAT formulation of the problem to successfully mine frequent flexible sequences occurring in transactional datasets. Our SAT-based approach can easily be extended with extra constraints to address a broad range of pattern mining applications. To demonstrate this claim, we formulate and add several constraints, such as gap and span constraints, to our model in order to extract more specific patterns. We also use interactive solving to perform important derived tasks, such as closed pattern mining or maximal pattern mining. Finally, we prove the practical feasibility of our SAT model by running experiments on two real datasets.

Motivation & Objective

• To address the inflexibility of traditional sequence mining algorithms that lack support for user-defined constraints.
• To demonstrate that SAT solvers can effectively handle the sequence mining problem by encoding it as a boolean formula.
• To enable the integration of diverse constraints—such as gap, span, and must-contain—into a single, extensible framework.
• To support derived mining tasks like closed and maximal pattern mining through interactive SAT solving.
• To evaluate the feasibility and performance of the SAT-based approach on real-world transactional datasets.

Proposed method

• The sequence mining problem is encoded as a pure boolean SAT formula, representing sequences and their embeddings in transactions using propositional variables.
• Constraints such as gap and span are formulated as additional boolean clauses to restrict valid embeddings and prune the search space.
• The must-contain constraint is encoded by requiring specific items to appear at specified positions in the sequence.
• Interactive SAT solving is used to iteratively query the solver, enabling the extraction of closed and maximal patterns without re-running the full mining process.
• The model is implemented using the Glucose SAT solver, leveraging its efficiency and incremental solving capabilities.
• The approach supports arbitrary combinations of constraints without compromising correctness or performance.

Experimental results

Research questions

• RQ1 Can the sequence mining problem be effectively formulated as a SAT problem to enable flexible constraint integration?
• RQ2 How does the inclusion of user-defined constraints such as gap, span, and must-contain affect solving performance and search space pruning?
• RQ3 Can interactive SAT solving be used to efficiently extract derived pattern types like closed and maximal patterns?
• RQ4 How does the SAT-based approach compare in performance to specialized algorithms on real-world datasets?
• RQ5 To what extent can the SAT model scale and remain efficient when handling complex, application-specific constraints?

Key findings

• The SAT-based approach successfully encodes flexible sequence mining as a boolean formula, enabling the use of off-the-shelf SAT solvers for pattern discovery.
• The addition of constraints such as gap and span significantly prunes the search space and reduces solving time, especially on larger datasets like T100.
• The combination of regular constraints with 2-gap constraints leads to a drastic reduction in mining time, demonstrating strong performance gains.
• On the Gazelle-500 dataset, where sequences are very short, gap and span constraints have minimal impact due to the small size of sequences, but do not degrade performance.
• Interactive solving enables efficient extraction of closed and maximal patterns without full re-computation, reducing redundancy in results.
• The approach is scalable and flexible, allowing users to combine arbitrary constraints without loss of correctness or significant performance penalty.