I am looking for a fast solution to the assignment problem for large cost matrices (5000x5000 or larger). The Hungarian algorithm is $O^3$, which is impractical for any moderately large problem. Are there similar algorithms but sub-optimal and fast, possibly in R (or Python)?
The problem I'm working consists of finding the best pairs of points in sets A and B (|A|=|B|), minimizing their overall distance.
