Abstract
In this paper we study the applicability of bucket elimination (BE) to the problem of finding still-life patterns. Very recently, it has been tackled using integer programming and constraint programming, both of them being search-based methods. We show that BE, which is based on dynamic programming, provides an exponentially lower worst-case time complexity than search methods. Unfortunately, BE requires exponential space, which is a disadvantage over the polynomial space requirement of depth-first search.
With our experiments, we show that BE is quite competitive with search-based approaches. It clearly outperforms simple encodings and it is comparable with dedicated methods. While the best current search approach solves the n=14 instance in about 6 cpu days, BE solves it in about 1 day. BE cannot solve the n=15 instance due to space exhaustion (this instance is solved by search in 8 days). Finally, we show how BE can be adapted to exploit the problem symmetries, with which in several cases we outperform previous results in a relaxation of the problem which restrict solutions to symmetric patterns, only.
The first author is supported by the REPLI project TIC-2002-04470-C03.
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Larrosa, J., Morancho, E. (2003). Solving ‘Still Life’ with Soft Constraints and Bucket Elimination. In: Rossi, F. (eds) Principles and Practice of Constraint Programming – CP 2003. CP 2003. Lecture Notes in Computer Science, vol 2833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45193-8_32
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DOI: https://doi.org/10.1007/978-3-540-45193-8_32
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