There seems to be a few theoretical options around at the moment for geometric simplification. Douglas–Peucker seems the most established, followed by Visvalingam's approach (used by d3.js). Now there's the relatively new 'Robust Douglas-Peucker' (Pallero?) method. I'm not clear what the relative merits are of these, and I've not had much luck finding libraries for the latter two in open-source environments (R, Python, etc) that would enable me to test them out.
So this question is primarily what open-source libraries can anyone point to for alternatives to the classic (but often problematic for topology preservation) Douglas–Peucker. But I think it would also be really useful to have any comments from people with experience of the relative strengths of these approaches, and any links to relevant resources discussing these.