Greedy metric minimum online matchings with random arrivals.

We consider online metric minimum bipartite matching problems with random arrival order and show that the greedy algorithm assigning each request to the nearest unmatched server is n-competitive, where n is the number of requests. This result is complemented by a lower bound exhibiting that the greedy algorithm has a competitive ratio of at least n(ln3−ln2)∕ln4≈n0.292, even when the underlying metric space is the real line.