Marin Bougeret, György Dósa, Noam Goldberg, Michael Poss

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider robust variants of the bin packing problem with uncertain item sizes. Specifically we consider two uncertainty sets previously studied in the literature. The first is budgeted uncertainty (the UΓ model), in which at most Γ items deviate, each reaching its peak value, while other items assume their nominal values. The second uncertainty set, the UΩ model, bounds the total amount of deviation in each scenario. We show that a variant of the Next-cover algorithm is a 2 approximation for the UΩ model, and another variant of this algorithm is a 2Γ approximation for the UΓ model. Unlike the classical bin packing problem, it is shown that (unless P = N P ) no asymptotic approximation scheme exists for the UΓ model, for Γ “1. This motivates the question of the existence of a constant approximation factor algorithm for the UΓ model. Our main result is to answer this question by proving a (polynomial-time) 4.5 approximation algorithm, based on a dynamic-programming approach.

Original languageEnglish
Pages (from-to)2534-2552
Number of pages19
JournalSIAM Journal on Discrete Mathematics
Issue number4
StatePublished - 2022

Bibliographical note

Funding Information:
˚Received by the editors November 3, 2021; accepted for publication (in revised form) June 5, 2022; published electronically October 24, 2022. A preliminary version of this work has been published in [7]. Funding: This research has benefitted from the support of the ANR project ROBUST (ANR-16-CE40-0018). :LIRMM, University of Montpellier, CNRS, Montpellier 34095, France (, ;Department of Mathematics, University of Pannonia, Veszpr\e'm 8200, Hungary (dosagy@almos. \S Department of Management, Bar-Ilan University, Ramat Gan 5290002, Israel (noam.goldberg@

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics.


  • Next-cover
  • approximation algorithms
  • bin-packing
  • dynamic programming
  • robust optimization


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