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Efficient Brute-force state space search for Yin-Yang puzzle

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Abstract

We propose an algorithm comprising some new techniques to efficiently search the entire state space of the Yin-Yang puzzle which is an NP-complete problem, by skipping invalid solutions ranges. The algorithm features efficient memory usage and parallel execution. More than 99% of the state space for most of the puzzle’s board sizes is skipped. It speeds up the process of finding valid solutions significantly. We were able to find all valid solutions in the space of more than 18 million billion states using a regular desktop PC. Another research about the Yin-Yang puzzle has examined the largest full-empty Yin-Yang board of size \(5\times 6\). Our proposed algorithm significantly improves performance. Using four parallel threads, it is 357 times faster than the regular and modified BFS and DFS algorithms used in that research, and it performs 192 times faster using a single thread. Our algorithm also consumes over 26,000 times less memory than the other algorithms.

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Data availability

The dataset and the application for viewing the results are available on GitHub.

Notes

  1. State space is the set of all possible states that the environment (like pieces in a Yin-Yang puzzle board) can be in. [3]

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Authors and Affiliations

  1. Department of Computer Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Kurdistan, Iran

    Arash Ahmadi & Amanj Khorramian

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  1. Arash Ahmadi
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  2. Amanj Khorramian
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Both authors have contributed equally to this work.

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Correspondence to Arash Ahmadi.

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We would like to express our sincere gratitude to the reviewers for their valuable comments and great suggestions that helped us improve the quality and clarity of our paper. We appreciate their time and effort in reviewing our work.

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Ahmadi, A., Khorramian, A. Efficient Brute-force state space search for Yin-Yang puzzle. J Supercomput 80, 3066–3088 (2024). https://doi.org/10.1007/s11227-023-05565-w

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