Online Graph Algorithms with Predictions

Yossi Azar, Debmalya Panigrahiy, Noam Touitou

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

Abstract

Online algorithms with predictions is a popular and elegant framework for bypassing pessimistic lower bounds in competitive analysis. In this model, online algorithms are supplied with future predictions and the goal is for the competitive ratio to smoothly interpolate between the best offine and online bounds as a function of the prediction error. In this paper, we study online graph problems with predictions. Our contributions are the following: The first question is defining prediction error. For graph/metric problems, there can be two types of error, locations that are not predicted, and locations that are predicted but the predicted and actual locations do not coincide exactly. We design a novel definition of prediction error called metric error with outliers to simultaneously capture both types of errors, which thereby generalizes previous definitions of error that only capture one of the two error types. We give a general framework for obtaining online algorithms with predictions that combines, in a \black box" fashion, existing online and offine algorithms, under certain technical conditions. To the best of our knowledge, this is the first general-purpose tool for obtaining online algorithms with predictions. Using our framework, we obtain tight bounds on the competitive ratio of several classical graph problems as a function of metric error with outliers: Steiner tree, Steiner forest, priority Steiner tree/forest, and uncapacitated/capacitated facility location. Both the definition of metric error with outliers and the general framework for combining offine and online algorithms are not specific to the problems that we consider in this paper. We hope that these will be useful for future work on other problems in this domain.

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2022
PublisherAssociation for Computing Machinery
Pages35-66
Number of pages32
ISBN (Electronic)9781611977073
StatePublished - 2022
Event33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States
Duration: 9 Jan 202212 Jan 2022

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2022-January

Conference

Conference33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Country/TerritoryUnited States
CityAlexander
Period9/01/2212/01/22

Funding

FundersFunder number
National Science FoundationCCF-1955703, CCF-1750140
Army Research OfficeW911NF2110230
Israel Science Foundation2304/20

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