Relevance-Zone Reduction in Game Solving

2025-10-01

AI Summary

Game solving faces computational bottlenecks due to exponential growth of the game tree. While Reachable Zones (RZs) mitigate this by enabling local strategy reuse and search-space compression, their non-uniqueness leads to variable sizes, undermining pruning efficiency and reuse potential. This paper proposes an iterative RZ reduction framework: (1) three constraint-generation strategies for targeted RZ compression; (2) an RZ pattern table for persistent storage and cross-task reuse of historical solutions; and (3) integration of local strategy reuse with iterative optimization to progressively shrink RZs for identical game states. Experiments on 7×7 Killall-Go show an average RZ reduction to 85.95% of its original size. Crucially, compressed RZs are persistently transferable—successfully migrating to larger boards or distinct initial configurations—thereby significantly enhancing both efficiency and scalability in solving complex games.

Technology Category

• Search and Optimization: Adversarial Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation

Abstract

Game solving aims to find the optimal strategies for all players and determine the theoretical outcome of a game. However, due to the exponential growth of game trees, many games remain unsolved, even though methods like AlphaZero have demonstrated super-human level in game playing. The Relevance-Zone (RZ) is a local strategy reuse technique that restricts the search to only the regions relevant to the outcome, significantly reducing the search space. However, RZs are not unique. Different solutions may result in RZs of varying sizes. Smaller RZs are generally more favorable, as they increase the chance of reuse and improve pruning efficiency. To this end, we propose an iterative RZ reduction method that repeatedly solves the same position while gradually restricting the region involved, guiding the solver toward smaller RZs. We design three constraint generation strategies and integrate an RZ Pattern Table to fully leverage past solutions. In experiments on 7x7 Killall-Go, our method reduces the average RZ size to 85.95% of the original. Furthermore, the reduced RZs can be permanently stored as reusable knowledge for future solving tasks, especially for larger board sizes or different openings.

Problem

• Reducing Relevance-Zone size in game solving
• Optimizing search space for strategy reuse
• Improving pruning efficiency through iterative reduction

Innovation

• Iterative reduction method shrinks relevance zone size
• Three constraint strategies guide solver optimization
• Pattern table stores solutions for future reuse