The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On the complexity of Jensen's algorithm for counting fixed polyominoes
Journal of Discrete Algorithms
Counting Polycubes without the Dimensionality Curse
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Redelmeier's algorithm for counting lattice animals
Proceedings of the twenty-seventh annual symposium on Computational geometry
Parallel enumeration of lattice animals
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
A polyominoes-permutations injection and tree-like convex polyominoes
Journal of Combinatorial Theory Series A
Counting d-dimensional polycubes and nonrectangular planar polyominoes
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Polyominoes on twisted cylinders
Proceedings of the twenty-ninth annual symposium on Computational geometry
The growth rate of high-dimensional tree polycubes
European Journal of Combinatorics
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The exact enumeration of most interesting combinatorial problems has exponential computational complexity. The finite-lattice method reduces this complexity for most two-dimensional problems. The basic idea is to enumerate the problem on small finite lattices using a transfer-matrix formalism. Systematically grow the size of the lattices and combine the results in order to obtain the desired series for the infinite lattice limit. We have developed a parallel algorithm for the enumeration of polyominoes, which are connected sets of lattice cells joined at an edge. The algorithm implements the finite-lattice method and associated transfer-matrix calculations in a very efficient parallel setup. Test runs of the algorithm on a HP server cluster indicates that in this environment the algorithm scales perfectly from 2 to 64 processors.