Well, I thought that providing code that actually attempts to solve the problem and that shows that the data is not valid would be useful to you and to others (even though it is only a partial validation, since it is looking at distances only to A, B and C, not to other points, but it is easy to extend it if needed).

It was fun anyway to try to solve the issue, in a subject-area quite far away from what I am doing daily with Perl. I enjoyed it. Thank you for that.

I thought that providing code that actually attempts to solve the problem ... would be useful to you and to others

It is/will be.

... and that shows that the data is not valid ...

However, the data is valid.

There is nothing in the definition of the TSP that says that the "distances" involved have to be mappable to a flat 2D plane. They could be great circle distances from a sphere; or roads that follow coast and river and skirt hills. They don't even need to be symmetrical! (Flight distances from New York to London can be substantially shorter (or longer) than that from London to New York depending upon the direction & strength of the prevailing wind.)

The desire to visualise data doesn't go away when the data itself is inconvenient.

It was fun anyway to try to solve the issue, in a subject-area quite far away from what I am doing daily with Perl. I enjoyed it. Thank you for that.

I'm glad for that; and for your help :)

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

I only meant not valid in the narrow framework of "the 'as the crow flies' distances into a set of 2D plane coordinates for plotting" set out in your original post. I fully appreciate that it surely can be valid in other contexts.