Online Bipartite Matching with Advice: Tight Robustness-Consistency Tradeoffs for the Two-Stage Model
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We study the two-stage vertex-weighted online bipartite matching problem of Feng, Niazadeh, and Saberi (SODA 2021) in a setting where the algorithm has access to a suggested matching that is recommended in the first stage. We evaluate an algorithm by its robustness R, which is its performance relative to that of the optimal offline matching, and its consistency C, which is its performance when the advice or the prediction given is correct. We characterize for this problem the Pareto-efficient frontier between robustness and consistency, which is rare in the literature on advice-augmented algorithms, yet necessary for quantifying such an algorithm to be optimal. Specifically, we propose an algorithm that is R-robust and C-consistent for any (R,C) with 0 ≤ R ≤3/4 and √(1-R) + √(1-C) = 1, and prove that no other algorithm can achieve a better tradeoff.
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