This is a common problem.

The user will be patient for about 20-30 seconds if you warn them about this in advance. Without any warning at all, the folks will just give up and cancel the browser session if the time goes past that. That frustrates everybody! They are angry and this burned a lot of Mips on your server to no result. Everybody is mad.

The idea of not producing a result at all is bad! WOW!
That is an incredibly bad idea!
Your program should produce a result, even if that result is "I can't produce a result".

I sometimes work with some large DB's on line, like the FCC, U.S. Federal Communications Commission (FCC.gov). I can submit a complex DB query and I give them an email to send the reply to. After maybe 30 minutes, I get a URL via email that allows me to download my results. That URL and the data "expires" after some amount of time (24-48 hours or so). This idea works very well for complicated things.

Of course the best thing is to be performant and generate a quick response, but that is not always possible.