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arXiv · 2112.07228

Online Matching with High Probability

Milena Mihail·Thorben Tröbst
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Abstract

We study the classical, randomized Ranking algorithm which is known to be $(1 - \frac{1}{e})$-competitive in expectation for the Online Bipartite Matching Problem. We give a tail inequality bound, namely that Ranking is $(1 - \frac{1}{e} - \alpha)$-competitive with probability at least $1 - e^{-2 \alpha^2 n}$ 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.

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Milena Mihail, Thorben Tröbst. 2021-12-14. Online Matching with High Probability. https://arxiv.org/abs/2112.07228

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