in reply to WEB host for Perl/CGI based site
The other people who have already posted are right when they say you can't do this on a regular (shared) hosting account. Most web hosts will figure out that somebody is using way too many resources, and they will suspend your account at the very least.
You should probably rethink how this page works. Perhaps you can run the script as a cron job, say once or twice daily, so that page requests would not be forced to reprocess the data, and could just spew the results.
Either way, to do processing required 1G RAM for 1-2 minutes, you probably will need either a Virtual Private Server (VPS) or a Semi-Dedicated (SDX) server.
I've gotta say that I'm curios what you have that needs to be private, that takes 1G of ram to process. Fixing that script up a bit will open up a lot more options for you in terms of hosting.