Online Bipartite Matching with Advice: Tight Robustness-Consistency Tradeoffs for the Two-Stage ModelDownload PDF

Published: 31 Oct 2022, Last Modified: 12 Mar 2024NeurIPS 2022 AcceptReaders: Everyone
Keywords: Online matching, online algorithms with advice, prediction augmented, learning augmented, two stage optimization
TL;DR: We characterize the tight robustness-consistency tradeoff for two-stage vertex-weighted bipartite matching with advice.
Abstract: We study the two-stage vertex-weighted online bipartite matching problem of Feng, Niazadeh, and Saberi (SODA ‘21) 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 $0 \leq R \leq \frac{3}{4}$ and $\sqrt{1-R} + \sqrt{1-C} = 1$, and prove that no other algorithm can achieve a better tradeoff.
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