Taming the Search Space: Solving and Generating Hitori and Binairo Puzzles

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.