[hnfong]

If you look carefully at the graph on the readme page, you'd see it compares Dijkstra's algorithm, a "DMMSY(res)", and a "DMMSY(opt)".

Presumably the claimed contribution was the optimized version, but note that whatever DMMSY(res) is, it should still be O(m log^{2/3} n) or whatever DMMSY's time complexity is supposed to be.

But DMMSY(res)'s run times follow Dijkstra closely in the graph.

The only conclusion is that something is off -- either the author measured the wrong thing, or he was able to optimize the implementation of the algorithm to the extent that the optimizations over-powers any asymptotic gains. Or the implementation is wrong.

At any rate, as you mentioned, the difference between `m log n` and `m log^{2/3} n` is insignificant at n=1M (and TBH won't be significant at any practical n). If the results and the implementation are both correct, it just means the author simply found a way to reduce the constant time factor of the implementation.