Prophet Matching with General Arrivals

Tomer Ezra, Michal Feldman, Nick Gravin, Zhihao Gavin Tang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We provide prophet inequality algorithms for online weighted matching in general (nonbipartite) graphs, under two well-studied arrival models: edge arrival and vertex arrival. The weights of the edges are drawn from a priori known probability distribution. Under edge arrival, the weight of each edge is revealed on arrival, and the algorithm decides whether to include it in the matching or not. Under vertex arrival, the weights of all edges from the newly arriving vertex to all previously arrived vertices are revealed, and the algorithm decides which of these edges, if any, to include in the matching. To study these settings, we introduce a novel unified framework of batched-prophet inequalities that captures online settings where elements arrive in batches. Our algorithms rely on the construction of suitable online contention resolution scheme (OCRS). We first extend the framework of OCRS to batched-OCRS, we then establish a reduction from batched-prophet inequality to batched-OCRS, and finally we construct batched-OCRSs with selectable ratios of 0.337 and 0.5 for edge and vertex arrival models, respectively. Both results improve the state of the art for the corresponding settings. For vertex arrival, our result is tight. Interestingly, a pricing-based prophet inequality with comparable competitive ratios is unknown.

Original languageEnglish
Pages (from-to)878-898
Number of pages21
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2022


FundersFunder number
Shanghai University of Finance and Economics, Program for Innovative Research Team
H2020 European Research Council866132
H2020 European Research Council
National Natural Science Foundation of China61902233
National Natural Science Foundation of China
Shanghai Municipal Education Commission
Israel Science Foundation317/17
Israel Science Foundation
Central Universities in China2018AAA0100903
Central Universities in China


    • online contention resolution scheme
    • online matching
    • online stochastic matching
    • prophet inequality


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