Abstract
We study the computational complexity of the puzzle Quell. The goal is to collect pearls by sliding a droplet of water over them in a grid map. The map contains obstacles. In each move, the droplet slides in one of the four directions to the maximal extent, until it is stopped by an obstacle. We show that any-Moves-all-Pearls (deciding whether it is possible to collect all the pearls using any number of moves) can be solved in polynomial time. In contrast, both any-Moves-max-Pearls (finding the maximum number of pearls that can be collected using any number of moves) and min-Moves-all-Pearls (finding the minimum number of moves required to collect all the pearls) are APX-hard, although the corresponding decision problems are in FPT. We also present a simple 2-approximation for any-Moves-max-Pearls, and leave open the question whether min-Moves-all-Pearls admits a polynomial-time constant approximation.
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Jiang, M., Tejada, P.J., Wang, H. (2014). Quell. In: Ferro, A., Luccio, F., Widmayer, P. (eds) Fun with Algorithms. FUN 2014. Lecture Notes in Computer Science, vol 8496. Springer, Cham. https://doi.org/10.1007/978-3-319-07890-8_21
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DOI: https://doi.org/10.1007/978-3-319-07890-8_21
Publisher Name: Springer, Cham
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