Should a highly dynamic website that is constantly generating new pages use a sitemap? If so, how does a site like stackoverflow.com go about regenerating a sitemap? It seem
There's no need to regenerate the Google sitemap XML each time a question is posted. It's far simpler just to have the XML file generated on-demand directly from the database (and a little caching).
To reduce load, the sitemap can be split into many sitemaps. Partitioning it by day/month would allow you to tell Google to retrieve today's sitemap frequently, but only fetch the sitemap from six months ago once in a while.