Collapsing a generic curve into a path graph help.

My problem is: the user draw generic path on a map and I must get this curve/line/path and "collapse"/approximate it to the paths (roads) on the map. I'm not asking for a direct easy solution, but I don't know where to start and my searches, so far, haven't got me anywhere. Is there a technical name for this I could use to search? Does anyone knows any similar solution I could look at?