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A Note on Domino Shuffling . Janvresse, T. de la Rue and Y. Velenik Electron. J. Combin. 13 (1), R30 (2006). We present a variation of James Propp's generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification is specially tailored to deal with cases when some of the weights are zero. This allows us to tile efficiently a large class of planar graphs, by embedding them in a large enough Aztec diamond. We also give a sufficient condition on the size of the latter diamond for the algorithm to succeed. Key words: Domino shuffling, Perfect matching, Random tiling, Random generation, Aztec Diamond. Files: PDF, published version, bibtex
Errata:PDF (new proof of Lemma 3, and a few typos corrected).