So, the title is a little awkward. I'll give some background, and then ask my question.
Background: I work as a web GIS application developer, but in my spare time I've been playing with map rendering and improving data interchange formats. I work only in 2D space.
One interesting issue I've encountered is that when you're rendering a polygon at a small scale (zoomed way out), many of the vertices are redundant. An extreme case would be that you have a polygon with 500,000 vertices that only takes up a single pixel. If you're sending this data to the browser, it would make sense to omit ~499,999 of those vertices. One way we achieve that is by rendering an image on a server and and sending it as a PNG: voila, it's a point. Sometimes, though, we want data sent to the browser where it can be rendered with SVG (or canvas, or webgl) so that it can be interactive.
The problem: It turns out that, using modern geographic data sets, it's very easy to overload SVG's rendering abilities. In an effort to cope with those limitations, I'm trying to figure out how to visually losslessly reduce a data set for a given scale and map extent (and, if necessary, for a known map pixel width and height).
I got a great reduction in data size just using the Douglas-Peucker algorithm, and I believe I was able to get it to keep the polygons true to within one pixel. Unfortunately, Douglas-Peucker doesn't preserve topology, so it changed how borders between polygons got rendered. I couldn't readily find other algorithms to try out and adapt to the purpose, but I don't have much CS/algorithm background and might not recognize them if I saw them.