Random rook's tour of a rectangle

*To*: mathgroup at smc.vnet.net*Subject*: [mg50284] Random rook's tour of a rectangle*From*: "DIAMOND Mark R." <dot at dot.dot>*Date*: Tue, 24 Aug 2004 06:22:34 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

[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