heh. this is fun.
that is fun. brought me back to my college days when I spent a good portion of junior fall semester writing a program to do just that. well, the human made the graphs and the computer's job was to solve it, and it was in 3d not 2d, but that's ok.
oh, i gave up at level 11. it was getting crowded.
The Tom DeMarco / Yourdon "Structured Analysis" approach developed software systems as a "sea of interconnected bubbles" -- this game would have been a wonderful way of 'untwisting' that sea of bubbles.
neat. the maths must be cool.
are solutions unique? do all problems of a given number of nodes have the same level of complexity/difficulty?
I guess the algorithm to solve is iterative, and involves finding the "outer ring" path for a given subset?
> do all problems of a given number of nodes have the same level of complexity/difficulty?
What does that mean? There are lots of non-planar graphs (see K5 and K(3,3)). Over a certain fairly small node size (10? 12?) most graphs aren't. Hence there's no solution.
In this case the computer generates planar graphs which is why it's not that hard to solve them (the main issue for humans becomes making enough space on the screen to move nodes around).
Arrgghhhh. It's the MS Access Relationships diagram.
You are in a twisty maze of little tables.
There is a misplaced link here.
I guess I mean how much work is taken to solve them. As any given graph can be presented either nearly solved or as a hellish tangle, the answer is "no, problems for a graph of a certain size are not all the same level of difficulty". Obvious now ...