Huge computer science result:
A Tsinghua professor JUST discovered the fastest shortest path algorithm for graphs in 40yrs.
This improves on Turing award winner Tarjan’s O(m + nlogn) with Dijkstra’s, something every Computer Science student learns in college.
@yosupot Hi yosupo, this can be improved to Omega~(N^1.5)? Roughly speaking, pick a random prime p ~ N^0.5 and group the numbers based on residues mod p (each group likely has size ~ N^0.5). Let each group occupy a contiguous subarray. There are only p^2 interesting triples of groups