[meetups323]

Quadratic doesn't need to equal "bad", especially in this case. Two 45 kB items is 2 billion entries. Allocating 2 billion bytes is easy enough. Iterating over 2 billion bytes is also not terrible. The GP says the process is estimated to take 150 hours, or half a million seconds, or 1.62e15 cycles... so around 1 million cycles per cell.

[dan-robertson]

If it’s doing anything nontrivial (eg computing the weights of the diagonal edges by comparing the rows as sequences) then you’re basically screwed. The problem with quadratic is that it doesn’t scale but it’s fast enough for small inputs that it is hard to notice until you get a large input.

[meetups323]

My point is that even though it's quadratic it can still be fast for the inputs mentioned (dozens of kilobytes), so long as the constant is low. If you have a quadratic algorithm that takes 1 cycle per byte of input squared(or less, using wide registers), it will be pretty damn quick for most inputs. If you have a quadratic algorithm that takes 1 million cycles for each byte of input squared (such as this one), that's a whole different story. The time to process 1 Megabyte in the 1 cycle algorithm would only let you process a kilobyte in the new.

Point is that things like being efficient with memory access and using sufficiently low level (or JIT'ed) languages can get you very far, and it's not really meaningful to dismiss an algorithm solely based on it being quadratic.