I don't suppose there is some advanced way to get an approximate count. When the number of items is so large it seems a little pointless to get an accurate count anyway; within 1% would be acceptable if there were a way to get it quickly.
This seems like something you could build yourself: - As a background task, periodically run the queries to compute the counts of interest, and store those count results in a special "pre-computed counts" table. - In places in your application where you are willing to tolerate an approximate count, fetch the pre-computed count from your special table. - Vary the period of re-computing the counts to control how accurate (that is, how recently re-computed) your counts are. The more often you re-compute the counts, the more accurate they will be, but the higher the overhead you'll see from the re-compute background task.
bryan
