Online Matching with High Probability

12/14/2021

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by   Milena Mihail, et al.

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We study the classical, randomized Ranking algorithm which is known to be (1 - 1/e)-competitive in expectation for the Online Bipartite Matching Problem. We give a tail inequality bound, namely that Ranking is (1 - 1/e - α)-competitive with probability at least 1 - e^-2 α^2 n where n is the size of the maximum matching in the instance. Building on this, we show similar concentration results for the Fully Online Matching Problem and for the Online Vertex-Weighted Bipartite Matching Problem.