🤖 AI Summary
This study addresses the challenge of the vast search space in solving and generating Hitori and Binairo logic puzzles by systematically comparing an optimized backtracking approach—integrating constraint propagation and heuristic variable ordering—with SAT-based methods. The work introduces the first unified framework for generating uniquely solvable instances of both puzzle types, enabling systematic benchmarking. This framework combines iterative connectivity checks with CNF encoding techniques. Experimental results demonstrate that constraint propagation substantially reduces search tree size; SAT solvers outperform other methods on Binairo, whereas the optimized backtracking algorithm achieves superior performance on Hitori. The proposed approaches provide efficient solutions for both puzzle generation and solving, while establishing a reproducible evaluation benchmark for future research.
📝 Abstract
This paper investigates solving and generation techniques for the logic puzzles Hitori and Binairo. Two solving paradigms are compared: backtracking with domain-specific optimizations, and SAT-based solving via conjunctive normal form encodings. An empirical evaluation analyzes runtime, explored search nodes, and branching factor across varying puzzle sizes. To support systematic benchmarking in the evaluation, generators capable of producing valid and uniquely solvable puzzle instances are developed. Results indicate that constraint propagation is the most effective backtracking optimization, substantially reducing the effective branching factor, search tree size, and thus runtime. Heuristic variable ordering and scoring strategies provide additional improvements. For Binairo, the SAT-based approach solves all evaluated instances within low runtime, while optimized backtracking fails to solve difficult puzzle instances within the timeout. For Hitori, propagation-based backtracking achieves the best results, while for the SAT-based approach the iterative connectivity check takes up the majority of the runtime, failing difficult puzzle instances.