[Paper Review] On SAT Models Enumeration in Itemset Mining

Saïd Jabbour, Lakhdar Saïs+1 more|arXiv (Cornell University)|Jun 8, 2015

Data Mining Algorithms and Applications21 references3 citations

TL;DR

This paper investigates the adaptation of CDCL-based SAT solvers for efficient enumeration of models in SAT-encoded frequent itemset mining. It finds that a simple DPLL-like procedure with the Jeroslow-Wang branching heuristic outperforms CDCL solvers with blocking clauses, especially on instances with many models, due to reduced overhead from clause learning and blocking mechanisms.

ABSTRACT

Frequent itemset mining is an essential part of data analysis and data mining. Recent works propose interesting SAT-based encodings for the problem of discovering frequent itemsets. Our aim in this work is to define strategies for adapting SAT solvers to such encodings in order to improve models enumeration. In this context, we deeply study the effects of restart, branching heuristics and clauses learning. We then conduct an experimental evaluation on SAT-Based itemset mining instances to show how SAT solvers can be adapted to obtain an efficient SAT model enumerator.

Motivation & Objective

• To improve the efficiency of SAT-based model enumeration in frequent itemset mining by adapting CDCL solver components.
• To investigate the impact of restarts, branching heuristics, and clause learning on model enumeration performance.
• To compare DPLL-like procedures with CDCL-based solvers augmented with blocking clauses for enumerating closed frequent itemsets.
• To identify the most effective solver configuration for SAT encodings of data mining problems with exponentially large output.
• To provide empirical evidence on the limitations of clause learning and blocking clauses in high-model-count scenarios.

Proposed method

• Implemented a DPLL-like model enumerator (DPLL-Enum) without blocking or learned clauses to isolate the effect of solver components.
• Extended the MiniSAT 2.2 CDCL solver with a model enumeration procedure (CDCL-Enum) that adds no-good clauses and triggers restarts after each model is found.
• Evaluated three branching heuristics: VSIDS, Jeroslow-Wang (JW), and random selection, within the DPLL-Enum framework.
• Used cactus plots to compare CPU time across multiple datasets from FIMI and CP4IM repositories, varying minimal support thresholds.
• Conducted experiments on Intel Xeon quad-core machines with 15-minute CPU time limits per instance.
• Measured performance across diverse real-world datasets, focusing on closed frequent itemset enumeration.

Experimental results

Research questions

• RQ1 How do restarts, branching heuristics, and clause learning affect the performance of SAT solvers in model enumeration for itemset mining?
• RQ2 Is the CDCL-based approach with blocking clauses and clause learning more efficient than a pure DPLL-like procedure for enumerating models in SAT-encoded itemset mining?
• RQ3 Which branching heuristic—VSIDS, Jeroslow-Wang, or random—yields the best performance in DPLL-like model enumeration for this problem?
• RQ4 Does the presence of exponentially many models in the SAT encoding make clause learning and blocking clauses counterproductive?
• RQ5 Can a lightweight DPLL-like procedure outperform state-of-the-art CDCL solvers in model enumeration tasks with high model counts?

Key findings

• The DPLL-like procedure (DPLL-Enum) outperformed the CDCL-based approach (CDCL-Enum) on the majority of instances, especially those with a large number of models.
• The DPLL-Enum+JW variant (Jeroslow-Wang heuristic) consistently outperformed both DPLL-Enum+VSIDS and DPLL-Enum+RAND across multiple datasets.
• On datasets like chess, kr-vs-kp, and splice-1, DPLL-Enum+JW significantly reduced enumeration time compared to other heuristics and the CDCL approach.
• CDCL-Enum and DPLL-Enum+RAND failed to complete enumeration on several instances within the 15-minute timeout, indicating poor scalability.
• The use of blocking clauses and clause learning in CDCL-Enum introduced significant overhead, making it impractical for high-model-count problems.
• The results suggest that clause learning and blocking clauses are detrimental in model enumeration when the number of models is large, favoring simpler DPLL-like strategies.