The claim of a 700,000x speedup makes me suspicious of pretty much everything else about the work.
That is why database servers usually have the fastest discs money can buy, as much memory as you can fit in there in order to keep as much data as possible in main memory and the largest possible caches to avoid hitting the relatively slow memory bus as often as possible. The situation becomes much worse if the database is not read-only because all changes have to be persisted and you have to hit the disc on every change.
Therefore I think using GPUs will buy you nothing for common database application - processor speed was never your problem. But this does not exclude the possibility that there are operation, for example correlating millions of data points from your data set, where the processing power of GPUs comes handy, but this is most likely not what you will see in one of your line of business applications.
The number 700,000 is probably the result of a highly tuned GPU implementation versus a general purpose CPU implementation. A quad-core Core i7 at 3.0 GHz has a theoretical peak performance of 96 GFLOPs [1], the currently fastest supercomputer peaks at 27,112,500 GFLOPS (Titan, 560,640 cores, 8.2 MW [2]). 700,000 times the mentioned Core i7 is still more than twice the performance of Titan, 67,200,000 GFLOPs.
[1] http://stackoverflow.com/questions/15655835/flops-per-cycle-... [2] http://www.top500.org/lists/2012/11/
I also have an itchy feeling that there may have been some confusion regarding conversions between "times" and "percent", possibly multiple times. [1]
Extrapolating that an iterative solution would take 40 days, without running it for 40 days, is tricky as well. Given multiple tweets in close proximity, PostGIS should benefit from caching the R-tree index.
I'm not assuming the inventor is doing these things, as his db prof was impressed, as well as CSAIL and the body awarding his prize. [2] I think, if anything, the reporting is intended to be high-level enough to have more broad appeal, which makes it more difficult for us to evaluate the results in a Gedankenversuch. "Reduce slowness here..."
[1] The sidebar says,'Some statistical algorithms run 70 times faster compared to CPU-based systems like MapReduce,' while the quote in the article says,'“The speed ups over PostGIS … I’m not an expert, and I’m sure I could have been more efficient in setting up the system in the first place, but it was 700,000 times faster,” Mostak said. “Something that would take 40 days was done in less than a second.”'
[2] Hey, logical fallacies do not necessarily mean the argument is wrong!
He's got an in-memory column store, so (AFAIK) those are immediate advantages over PostGIS. He's also using pre-rendering of shapes into bitmaps (a form of caching/indexing) along with GPU hardware to accelerate intersection queries. It looks like this is a case where a problem (2D geo data) maps quite naturally to GPU hardware (2D textures) if only you can discover the mapping.