“Who is Next in Line?” On the Significance of Knowing the Arrival Order in Bayesian Online Settings

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We introduce a new measure for the performance of online algorithms in Bayesian settings, where the input is drawn from a known prior, but the realizations are revealed one-by-one in an online fashion. Our new measure is called order-competitive ratio. It is defined as the worst case (over all distribution sequences) ratio between the performance of the best order-unaware and order-aware algorithms, and quantifies the loss that is incurred due to lack of knowledge of the arrival order. Despite the growing interest in the role of the arrival order on the performance of online algorithms, this loss has been overlooked thus far. We study the order-competitive ratio in the paradigmatic prophet inequality problem, for the two common objective functions of (i) maximizing the expected value, and (ii) maximizing the probability of obtaining the largest value; and with respect to two families of algorithms, namely (i) adaptive algorithms, and (ii) single-threshold algorithms. We provide tight bounds for all four combinations, with respect to deterministic algorithms. Our analysis requires new ideas and departs from standard techniques. In particular, our adaptive algorithms inevitably go beyond single-threshold algorithms. The results with respect to the order-competitive ratio measure capture the intuition that adaptive algorithms are stronger than single-threshold ones, and may lead to a better algorithmic advice than the classical competitive ratio measure.

Original languageEnglish
Title of host publication34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023
PublisherAssociation for Computing Machinery
Number of pages18
ISBN (Electronic)9781611977554
StatePublished - 2023
Event34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023 - Florence, Italy
Duration: 22 Jan 202325 Jan 2023

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference34th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2023


FundersFunder number
NSF-BSF788893, 2020788
Horizon 2020 Framework Programme866132
European Research Council
National Natural Science Foundation of China61902233, 62150610500
Shanghai Municipal Education Commission
Ministero dell’Istruzione, dell’Università e della Ricerca
Israel Science Foundation317/17
Shanghai University of Finance and Economics
Fundamental Research Funds for the Central Universities


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