> “This thing might as well have been discovered 50 years ago, but it wasn’t,” Thorup said. “That makes it that much more impressive.”
this is so cool to me, it feel like a solution you could* have stumbled upon while doing game development or something
*probably wouldn't but still
Rather than the academia.
Just a hunch tho
Merge sort is supposedly invented in 1950, it’s more likely it was invented in 1050 than 1950. Sort a room full of documents for me. You have three minions, go.
But a room of five clerks all taking tasks off a pile and then sorting their own piles is merge sort at the end of the day. Literally, and figuratively.
We give a deterministic O(mlog2/3n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the O(m+nlogn) time bound of Dijkstra's algorithm on sparse graphs, showing that Dijkstra's algorithm is not optimal for SSSP.
Also the curently best factorization algorithm (GNFS) is at exp(k*log(n)^1/3log(log(n))^2/3).
Intro algorithms classes just tend to stay away from the really cursed runtimes since the normal ones are enough to traumatize the undergrads.
But if you're not implementing AI or game engines, some of the linear algebra space may be a road less traveled.
Im most curiosity how the algorithm fulfil the "global minima" that djixtra guarantees. The clumping of front-tier nodes seem prone to missing some solutions if unlucky.
Additionally, the `n` in the complexity only matters if for the Dijkstra approach you actually need a frontier of size proportional to `n` [remember that for open-grid-like graphs, the frontier is limited is limited to `sqrt(n)` for a plane, and for linear-ish graphs, the frontier is even more limited].
Also note that the "sorting barrier" only applies to comparison-based sorts, not e.g. various kinds of bucket sorts (which are easy to use when your weights are small integers). Which seems to be part of what this algorithm does, though I haven't understood it fully.
ljlolel•12h ago
larodi•11h ago
kzrdude•11h ago
bob1029•11h ago
https://en.wikipedia.org/wiki/Splay_tree
teraflop•9h ago
His Turing award writeup gives a pretty broad overview of his research contributions: https://amturing.acm.org/award_winners/tarjan_1092048.cfm