I have had the same question ever since I first heard about the Match. The computer shouldn't take more than a few minutes to run the algorithm. I have heard that there is "insider trading" that goes on between programs, similar to how professional sports teams trade draft picks. Basically, the Match is a draft.
However, this is highly unlikely since someone would have had to leak some information at some time since the Match was started, and it ruins the integrity that the Match is supposed to preserve. Another theory is that it really did take a long time for the old computers to run the algorithm back in the 50's or 60's when the Match was created. However, the gap in time has been preserved over the years basically as a remnant of tradition.
If the insider trading theory is true, I want some professional athelete salaries as part of the Match too!