[timtadh]

From a purely practical standpoint it means it is more tractable to solve large instances exactly. You can always wait for an answer but if you need more memory than you have you are out of luck. For instance, let's say before you had a problem of size 64. 2^64 bytes in gigabytes is 10^10 gigabytes. That is more ram than I have. However, a constant multiple (say 1,000,000,000) gives only 64 gigabytes. That takes an intractable problem to a tractable problem on a server with a large amount of memory. Yes, you still have to wait for the solution (maybe a long time) but at least you would have a hope of actually solving it.

[JadeNB]

> You can always wait for an answer but if you need more memory than you have you are out of luck.

I'm not a practical programmer, so I may be off base, but it seems to me that one could as well say "You can always buy more memory, but if the answer takes more time than you have to wait then you're out of luck." (In both cases, super-rapid growth won't take too long to exhaust the age, and the information capacity, of the universe.) Is it really clear that it's better to err on the side of more time in the time / space trade-off?

[AstralStorm]

No, because accessing memory also takes a lot of time. This is especially true on small machines like cellphones.