A dual graph translation of a problem in ‘Life (2002) [6 citations — 1 self]
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Abstract:
Abstract. Conway's game of Life provides interesting problems in which modelling issues in constraint programming can be explored. The problem of finding a maximum density stable pattern (`still-life') is discussed. A formulation of this problem as a constraint satisfaction problem with 0-1 variables and non-binary constraints is compared with its dual graph translation into a binary CSP. The success of the dual translation is surprising, since it has as many variables as the non-binary CSP and very large domains. An important factor is the identification of many redundant constraints: it is shown that these can safely be removed if arc consistency is maintained during search. The dual variables represent 3 \Theta 3 squares, and further improvements are found by basing both the search and bounds on the cost of completing a partial solution on a partition into such squares. 1
Citations
| 213 | Tree clustering for constraint networks – Dechter, Pearl - 1989 |
| 96 | The fantastic combinations of John Conway’s new solitaire game ‘Life’ Sci – Gardner - 1970 |
| 91 | Arc consistency for general constraint networks: Preliminary results – Bessière, Régin - 1997 |
| 70 | On the conversion between non-binary and binary constraint satisfaction problems – Bacchus, Beek - 1998 |
| 28 | Encodings of Non-Binary Constraint Satisfaction – Stergiou, Walsh - 1999 |
| 20 | Symmetry Breaking During Search – Gent, Smith |
| 5 | Constraint programming and hybrid formulations for life – Bosch, Trick - 2001 |
| 4 | Maximum density stable patterns in variants of Conway’s game of Life – Bosch - 2000 |
