Hypergraph Neural Networks Accelerate MUS Enumeration
Summary: arXiv:2604.09001v1 Announce Type: new
Abstract: Enumerating Minimal Unsatisfiable Subsets (MUSes) is a fundamental task in constraint satisfaction problems (CSPs). Its major challenge is the exponential growth of the search space, which becomes particularly severe when satisfiability checks are expensive. Recent machine learning approaches reduce this cost for Boolean satisfiability problems but rely on explicit variable-constraint relationships, limiting their application domains. This paper proposes a domain-agnostic method to accelerate MUS enumeration using Hypergraph Neural Networks (HGNNs). The proposed method incrementally builds a hypergraph with constraints as vertices and MUSes enumerated until the current step as hyperedges, and employs an HGNN-based agent trained via reinforcement learning to minimize the number of satisfiability checks required to obtain an MUS. Experimental results demonstrate the effectiveness of our approach in accelerating MUS enumeration, showing that our method can enumerate more MUSes within the same satisfiability check budget compared to conventional methods.
Introduction
In the field of artificial intelligence and constraint satisfaction problems, the task of enumerating Minimal Unsatisfiable Subsets (MUSes) is crucial. MUSes play a significant role in understanding the limitations of a given problem and in enhancing the efficiency of problem-solving algorithms. However, the challenge lies in the exponential growth of the search space, which can lead to significant computational burdens, especially when satisfiability checks are costly.
Current Challenges
Traditional methods for MUS enumeration often struggle with the scale and complexity of modern constraint satisfaction problems. While recent advancements in machine learning aim to streamline the process for Boolean satisfiability problems, they frequently depend on predefined variable-constraint relationships. This reliance constrains their applicability across various problem domains, limiting their utility in broader contexts.
Proposed Solution
The authors of the new paper introduce a novel approach that utilizes Hypergraph Neural Networks (HGNNs) to enhance the process of MUS enumeration. Unlike traditional systems, this method is designed to be domain-agnostic, making it versatile for a wide range of CSPs. The key components of the proposed approach include:
- Incremental Hypergraph Construction: The method constructs a hypergraph where constraints are represented as vertices and the MUSes identified up to each step are encoded as hyperedges.
- HGNN-Based Agent: The system employs an HGNN-based agent that is trained using reinforcement learning techniques, aimed at minimizing the number of satisfiability checks needed to identify an MUS.
Experimental Results
The authors conducted a series of experiments to evaluate the effectiveness of their approach. The results indicated a significant improvement in the speed and efficiency of MUS enumeration. Specifically, the proposed method demonstrated the ability to enumerate a greater number of MUSes within the same budget of satisfiability checks when compared to conventional enumeration methods.
Conclusion
The introduction of Hypergraph Neural Networks for the task of MUS enumeration represents a significant advancement in the field of constraint satisfaction problems. By reducing the reliance on explicit variable-constraint relationships and employing a more adaptable approach, this method opens up new avenues for research and application in AI. The promising experimental results suggest that further exploration and development could lead to even more efficient solutions for complex problem-solving tasks in the future.