In arxiv:cs.CG/0609033 I and my co-authors looked at a similar problem of choosing colors to visualize a partition of the plane into regions that might be disconnected. The point of view we ended up taking was that each region should have its own color, that these colors should all be chosen as visually distinct as possible, and that colors of neighboring pairs of cantons should be chosen to have especially strong contrast in order to make the borders stand out. We then modeled this as a problem of embedding the adjacency graph of the map into three-dimensional color space. Here’s a blog post with the resulting visualization.

I hope you got to see the debugged version of it all – Michael and Rahul pointed out quite critical bugs in it.

I used Graphviz on MacOSX to render the graphs – and the algorithm occasionally mirrors the geography, but much of it follows from the spring dynamics engine. I didn’t rearrange anything.

I am aware that the recolored map will be unintelligible – which was part of my point of wanting to draw it that way: show exactly how bad a decision that would have been.

I’m curious what program you used to render the .dot file, and did it produce that output directly, or did you manually rearrange the nodes to approximate the actual geography?

I would recolor the Liechtenstein map using this color choice, but I haven’t gotten around to installing a decent picture editing program just yet. That’ll have to wait.

If you do so, the result will be quite unintelligible. There will be no adjacent regions that share a color, but there will be no way of guessing which like-colored regions are actually parts of the same commune.