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Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2022

Constant-Ratio Approximation for Robust Bin Packing with Budgeted Uncertainty

Marin Bougeret
Noam Goldberg
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Michael Poss

Résumé

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

hal-02119351 , version 1 (03-05-2019)
hal-02119351 , version 2 (11-02-2020)
hal-02119351 , version 3 (30-10-2020)

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Marin Bougeret, György Dósa, Noam Goldberg, Michael Poss. Constant-Ratio Approximation for Robust Bin Packing with Budgeted Uncertainty. SIAM Journal on Discrete Mathematics, 2022, 36 (4), ⟨10.1137/21M1457199⟩. ⟨hal-02119351v3⟩
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