> By applying the longest-chain bound and the extreme-cut shortcut, the compile-time cliff in GHC’s optimal path can be effectively eliminated— and the dense worst case that survives is, satisfyingly, deeply mirrors nature’s own computational machinery.
So this can actually be implemented in GHC? I've only read through this once so far and not understood more than ¼, but the section right before the conclusion made it seem like the best you can do is O(n^2.82) along with a huge constant.
Author here: yeah the end result is that you wouldn’t actually want to do it in practice. Who wants to build a load of linear algebra into GHC, after all? But it was pleasing to show that you could make the algorithm subcubic if you really wanted. to.
> By applying the longest-chain bound and the extreme-cut shortcut, the compile-time cliff in GHC’s optimal path can be effectively eliminated— and the dense worst case that survives is, satisfyingly, deeply mirrors nature’s own computational machinery.
So this can actually be implemented in GHC? I've only read through this once so far and not understood more than ¼, but the section right before the conclusion made it seem like the best you can do is O(n^2.82) along with a huge constant.
Author here: yeah the end result is that you wouldn’t actually want to do it in practice. Who wants to build a load of linear algebra into GHC, after all? But it was pleasing to show that you could make the algorithm subcubic if you really wanted. to.