The authors tackle a century-old geometry problem by proving that every set of 30 points includes an empty hexagon. They optimize their encoding to reduce computational costs and validate their results through rigorous verification processes. The study demonstrates the power of SAT solving in solving complex mathematical problems efficiently.
The research builds upon historical explorations of unavoidable shapes in planar point sets and highlights the significance of efficient encoding strategies in SAT solving. By partitioning the problem into smaller subproblems, the authors achieve substantial speedups and provide insights into optimizing problem-solving approaches.
The study also delves into the intricacies of orientation variables, containment variables, and hole constraints to establish the existence of empty hexagons within point sets. Through meticulous optimization and symmetry-breaking techniques, the authors enhance the efficiency and accuracy of their computations.
Overall, this research sheds light on the innovative application of SAT solving in resolving long-standing mathematical problems and underscores the importance of thorough validation processes to ensure result accuracy and reliability.
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Önemli Bilgiler Şuradan Elde Edildi
by Marijn J.H. ... : arxiv.org 03-04-2024
https://arxiv.org/pdf/2403.00737.pdfDaha Derin Sorular