hungarian-algorithm-n3
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20 hours ago •
maandree
maandree
[Complete] 𝓞(n³) implementation of the Hungarian algorithm
𝓞(n³) implementation of the Hungarian algorithm, also known as the Hungarian method, Kuhn–Munkres algorithm or Munkres assignment.
The Hungarian algorithm solves the minmum 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 elements values are bounded within the priority queue's capacity. However this implemention achives 𝓞(n³) by not using a priority queue.
Edmonds and Karp, and independently Tomizawa, has also reduced the time complexity to 𝓞(n³), but I do not known how.
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