Abstract
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.
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Jensen, I. (2003). Counting Polyominoes: A Parallel Implementation for Cluster Computing. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J.J., Zomaya, A.Y. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44863-2_21
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