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{\bf \'E. Janvresse, T. de la Rue and Y. Velenik}
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{\bf A Note on Domino Shuffling}
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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.
\bye