Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: finite maze solving algorithm
Replies: 9   Last Post: Dec 3, 2004 7:09 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
conesetter

Posts: 115
Registered: 12/8/04
Re: finite maze solving algorithm
Posted: Dec 1, 2004 1:59 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


michalchik@aol.com (Michael Michalchik) wrote in message news:<20f4bb84.0411301849.18c69d1b@posting.google.com>...
> Kevin Saff <news@kevin.saff.net> wrote in message news:<I808DL.GF2@news.boeing.com>...
> > Michael Michalchik wrote:
> > > I was wondering if anyone knows if all possible topologies of finite
> > > 2d mazes can be solved by a finite algorithm. For example, we know
> > > that all fully connected mazes can be solved by picking a wall and
> > > exhaustively following it. Can a general solution work for all mazes
> > > including the ones that are piecewise disconnected? If this is
> > > possible, is the general solution a solved problem?
>
A maze with n walls is homeomorphic to the n-times punctured plane.
So the method of cuts used by Cauchy to derive a simply-connected
domain can be applied. The cuts in this instance become barriers
joining the walls in some sequence, the last one getting a final
barrier going off to infinity. Then any two points in the maze can be
joined by a path which is homotopically unique.
The method of Tremaux noted in the Wikipedia Maze article may amount
to the same thing but with the barriers introduced on the run rather
than in advance.




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.