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Random rook's tour of a rectangle


[I am not clear if this can be related to Mathematica, but I am permitting
 the post in case some can do it with Mathematica - moderator]

I wondered if anyone might know of an algorithm for generating a random
"rooks's tour" of a (not necessarily square) chessboard. I have looked in
the literature on self-avoiding walks tours of chessboards but not found
what I seek. (Knight's tour obviously gets a lot of attention).

I have found some exhaustive enumeration algorithms which cope with
relatively small chessboards, but none that find a random paths, and none
that would manage with, say, a 1000*1000 chessboard.

Any hints, algorithm, reference, suggestions for modifying an existing
algorithm (etc.) would be most appreciated.

Thanks,

--
Mark R. Diamond





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