Solving 'Still Life' with soft constraints and bucket elimination

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 worstcase 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 searchbased 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. © Springer-Verlag 2003.