𝓞(n³) implementation of the Hungarian algorithm, also known as the Hungarian method, Kuhn–Munkres algorithm or Munkres assignment. The Hungarian algorithm solves the minimum bipartite matching problem in 𝓞(n⁴). By implementing the priority queue with a van Emde Boas tree the time can be reduced to 𝓞(n³ log log n). The van Emde Boas tree is possible to use because the element values are bounded within the priority queue's capacity. However, this implementation achieves 𝓞(n³) by not using a priority queue. Edmonds and Karp, and independently Tomizawa, have also reduced the time complexity to 𝓞(n³), but I do not know how.
