Online Bipartite Matching with Amortized O(log 2 n) Replacements

@article{Bernstein2019OnlineBM,
  title={Online Bipartite Matching with Amortized O(log 2 n) Replacements},
  author={Aaron Bernstein and Jacob Holm and Eva Rotenberg},
  journal={Journal of the ACM (JACM)},
  year={2019},
  volume={66},
  pages={1 - 23}
}
In the online bipartite matching problem with replacements, all the vertices on one side of the bipartition are given, and the vertices on the other side arrive one-by-one with all their incident edges. The goal is to maintain a maximum matching while minimizing the number of changes (replacements) to the matching. We show that the greedy algorithm that always takes the shortest augmenting path from the newly inserted vertex (denoted the SAP protocol) uses at most amortized O(log 2 n… 
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