http://www.astrolog.org/labyrnth/algrithm.htm#perfect http://www.astrolog.org/labyrnth/algrithm.htm#perfect says that both the Aldous-Broder and Wilson's algori

http://www.astrolog.org/labyrnth/algrithm.htm#perfect http://www.astrolog.org/labyrnth/algrithm.htm#perfect says that both the Aldous-Broder and Wilson's algorithms will generate "all possible Mazes of a given size with equal probability". But neither meets your criteria of "efficient", since neither is even guaranteed to finish. I'm curious, too, whether there is an efficient algorithm with the same property (generate any valid maze with equal probability).