[Paper Review] Mini-Bucket Heuristics for Improved Search

Kalev Kask, Rina Dechter|arXiv (Cornell University)|Jan 23, 2013

Machine Learning and Algorithms13 references21 citations

TL;DR

This paper introduces mini-bucket heuristics to enhance search efficiency in constraint reasoning, generating high-quality heuristics via the mini-bucket elimination approximation scheme. Evaluated in Best-First search, the approach achieves superior performance over Branch-and-Bound when sufficient memory is available, demonstrating a controlled tradeoff between preprocessing and search cost on coding and medical diagnosis problems.

ABSTRACT

The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently introduced. The first paper introduced the idea and evaluated it within Branch-and-Bound search. In the current paper the idea is further extended and evaluated within Best-First search. The resulting algorithms are compared on coding and medical diagnosis problems, using varying strength of the mini-bucket heuristics. Our results demonstrate an effective search scheme that permits controlled tradeoff between preprocessing (for heuristic generation) and search. Best-first search is shown to outperform Branch-and-Bound, when supplied with good heuristics, and sufficient memory space.

Motivation & Objective

• To develop a systematic method for generating effective search heuristics automatically from approximation schemes.
• To evaluate the performance of these heuristics in Best-First search, contrasting them with Branch-and-Bound.
• To analyze the tradeoff between preprocessing cost (for heuristic generation) and search cost in practical reasoning tasks.
• To assess the scalability and effectiveness of mini-bucket heuristics on real-world problems such as coding and medical diagnosis.
• To demonstrate that high-quality heuristics derived from mini-bucket elimination can significantly reduce search effort when memory is sufficient.

Proposed method

• Utilizes the mini-bucket elimination algorithm as a foundation for approximating the optimal solution cost.
• Extracts heuristic values from the mini-bucket approximation to guide search, particularly for Best-First search strategies.
• Applies varying levels of approximation strength (i.e., different bucket sizes) to generate heuristics with controlled precision.
• Employs Best-First search with the generated heuristics to explore the search space more efficiently than Branch-and-Bound.
• Compares search performance across different approximation strengths to evaluate the tradeoff between preprocessing and search cost.
• Uses problem instances from coding and medical diagnosis domains to empirically validate the approach.

Experimental results

Research questions

• RQ1 Can mini-bucket heuristics generated via approximation schemes improve search performance in Best-First search compared to traditional Branch-and-Bound?
• RQ2 How does the strength of the mini-bucket approximation affect the quality of the resulting heuristics and search efficiency?
• RQ3 What is the tradeoff between the computational cost of heuristic generation and the reduction in search effort?
• RQ4 In what conditions does Best-First search outperform Branch-and-Bound when using high-quality heuristics?
• RQ5 How scalable and effective are mini-bucket heuristics on real-world reasoning problems like medical diagnosis and coding tasks?

Key findings

• Best-First search with mini-bucket heuristics outperforms Branch-and-Bound when sufficient memory is available and high-quality heuristics are used.
• The use of stronger mini-bucket approximations leads to better heuristic quality and reduced search effort, demonstrating a clear benefit from increased preprocessing.
• A controlled tradeoff between preprocessing cost and search cost is achievable by adjusting the approximation strength in mini-bucket elimination.
• The proposed heuristic generation method effectively leverages approximation to guide search without requiring problem-specific tuning.
• Empirical results on coding and medical diagnosis problems confirm that mini-bucket heuristics significantly reduce the number of nodes explored during search.
• The approach shows consistent performance gains across diverse problem instances, validating its general applicability in constraint reasoning tasks.