[unnah]

Euclidean TSP is easier than general symmetric TSP. Polynomial-time approximation schemes (PTAS) were discovered in parallel by Arora (1998) and Mitchell (1999). AFAIK those algorithms are not very practical though. I haven't followed subsequent work in any detail, but I haven't heard of any major breakthroughs since then.

[jhgb]

Well, damn. I imagine the reason why didn't know about this is because I have never been able to formulate any of my particular problems in terms of Euclidean TSP (even just metric was hard enough at times), so all interesting stuff was about metric TSP for me. I'll have to look at that work, though. Thanks for the pointers.