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Online Bin Covering with Frequency Predictions

Authors Magnus Berg , Shahin Kamali

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ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Online learning algorithms
  • Theory of computation → Online algorithms
Keywords
  • Bin Covering
  • Online Algorithms with Predictions
  • PAC Learning
  • Learning-Augmented Algorithms

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Abstract

We study the bin covering problem where a multiset of items from a fixed set S ⊆ (0,1] must be split into disjoint subsets while maximizing the number of subsets whose contents sum to at least 1. We focus on the online discrete variant, where S is finite, and items arrive sequentially. In the purely online setting, we show that the competitive ratios of best deterministic (and randomized) algorithms converge to 1/2 for large S, similar to the continuous setting. Therefore, we consider the problem under the prediction setting, where algorithms may access a vector of frequencies predicting the frequency of items of each size in the instance. In this setting, we introduce a family of online algorithms that perform near-optimally when the predictions are correct. Further, we introduce a second family of more robust algorithms that presents a tradeoff between the performance guarantees when the predictions are perfect and when predictions are adversarial. Finally, we consider a stochastic setting where items are drawn independently from any fixed but unknown distribution of S. Using results from the PAC-learnability of probabilities in discrete distributions, we introduce a purely online algorithm whose average-case performance is near-optimal with high probability for all finite sets S and all distributions of S.

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Magnus Berg and Shahin Kamali. Online Bin Covering with Frequency Predictions. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SWAT.2024.10

Author Details

Magnus Berg
  • University of Southern Denmark, Odense, Denmark
Shahin Kamali
  • York University, Toronto, Canada

Funding

  • Berg, Magnus: Supported in part by the Independent Research Fund Denmark, Natural Sciences, grant DFF-0135-00018B and in part by the Innovation Fund Denmark, grant 9142-00001B, Digital Research Centre Denmark, project P40: Online Algorithms with Predictions.
  • Kamali, Shahin: Supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC) [funding reference number DGECR-2018-00059].

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