<p>Just an idea. Why not throw some bots in there in the monte carlo fashion.
Let's call the first generation of bots gen0.
We only keep the bots from gen0 that have some continuous roads in this way:
<br>-from the start to some point
<br>or -from some point to the end</p>

<p>We run a new gen1 of bots in new random dots, then we try to connect the roads of the bots of gen1 with those of gen0 and see if we get a continous road from start to finish.</p>

<p>So for genn we try to connect with the bots form gen0, gen1, ..., genn-1.</p>

<p>Of course a generation lasts only a feasibil finit amount of time.</p>

<p>I don't know if the complexion of the algorithm will prove to be practical for small data sets.
<br>Also the algorithm assumes we know start and finish points.</p>

<p><br> some good sites for ideas:
<br> <a href="http://citeseerx.ist.psu.edu/" rel="nofollow noreferrer">http://citeseerx.ist.psu.edu/</a>
<br> <a href="http://arxiv.org/" rel="nofollow noreferrer">http://arxiv.org/</a></p>
Programming theory: Solve a maze
<p>What are the possible ways to solve a maze?<br>
Ive got two ideas, but I think they are not very elegant.</p>

<p><strong>Base situation:</strong> We have a matrix, and the elements in this matrix are ordered in a way that it represents a maze, with one way in, and one out.</p>

<p>My first idea was to send a robot through the maze, following one side, until it's out of the maze. I think this is a very slow solution.</p>

<p>The second one passes through every successive item marked with 1, checks where it can go (up, right, down, left) chooses one way and it continues its path there. This is even slower than the first one.</p>

<p>Of course it's a bit faster if I make the two bots multi-threaded at every junction, but thats also not the best way.</p>

<p>There needs to be better solutions to send a bot through a maze.</p>

<p><strong>EDIT</strong><br>
First: Thanks for the nice answers!</p>

<p><strong>The second part of my question is:</strong> What to do in the case if we have a multi-dimensional graph? Are there special practices for that, or is the answer of Justin L. usable for that too?<br>
I think it's not the best way for this case.</p>

<p><strong>The third question:</strong><br>
Which of these maze solver algorithms is/are the fastest? (Purely hypothetically)</p>