Joining the dots

*What* do you work at?

What you are describing sounds a lot like the Travelling Salesman Problem, a classic math puzzler that has never to my knowlege been solved. Martin Skidmore was in higher maths, IIRC. He may be able to correct me or supply a better answer to your question.

I did maths at Cambridge for one term. Mark S and Toby, probably among others, are far, far more knowledgeable. This does sound as if it may be in the same class, though the rules aren't defined tightly enough to say for sure. The Travelling Salesman problem does not seem susceptible to any elegant solution, and the brute force algorithms tend to become more cumbersome exponentially (I think that's right - NP, non-polynomial, isn't it?) with the number of nodes. It's one of those that anyone can do with three cities, a decent computer can do with a dozen, but it spirals out of control soon after.

I believe that there are solutions that provide good (not perfect) solutions to these problems in reasonable time. I'd have to dig out the couple of books I have on complexity theory to look out the details, but Toby probably knows off the top of his head.

No, no don't go to any trouble. I wilt just do the best I can using common sense I guess, it's just a timewasting work project and I thought I could speed things up. Thanks very much though.

If what yr. asking is finding the LONGEST distance between any two points, (as opposed to the shortest path between two particular points) then I think there is a simple rule, but I forget.