Approximation Results for Makespan Minimization with Budgeted Uncertainty

Bougeret, Marin; Jansen, Klaus; Poss, Michaël; Rohwedder, Lars

doi:10.1007/978-3-030-39479-0_5

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…Further, in the current paper it is proved that approximation results of standard bin packing in the form of asymptotic approximation scheme, cannot carry over (unless P = N P) to the robust counterpart with U Γ . While in previous papers [10,9] (with authors in common) we provided approximability results on robust scheduling, no such results have yet been proposed for the bin packing problem, the only previous work focusing on numerical algorithms [25]. The purpose of this paper is to fill these gaps, as we present constant-factor approximation algorithms the bin packing problem, both for U Ω and U Γ .…”

Section: Robust Bin Packing (Rbp)mentioning

confidence: 97%

Constant-Ratio Approximation for Robust Bin Packing with Budgeted Uncertainty

Bougeret¹,

Dósa²,

Goldberg³

et al. 2022

SIAM J. Discrete Math.

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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 U Γ 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 U Ω 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 U Ω model, and another variant of this algorithm is a 2Γ approximation for the U Γ model. Unlike the classical bin packing problem, it is shown that (unless P = N P) no asymptotic approximation scheme exists for the U Γ model, already for Γ = 1. This motivates the question of the existence of a constant approximation factor algorithm for the U Γ 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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Section: Robust Bin Packing (Rbp)mentioning

confidence: 97%

Constant-Ratio Approximation for Robust Bin Packing with Budgeted Uncertainty

Bougeret¹,

Dósa²,

Goldberg³

et al. 2022

SIAM J. Discrete Math.

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show abstract

“…Interestingly, these positive results do not extend to most scheduling problems (because they involve nonlinearities) and to the bin packing problem (because it involves a non-constant numbers of robust constraints). While in previous papers [13,12] (with authors in common) we provided approximability results on robust scheduling, no such results have yet been proposed for the bin packing problem, the only previous work focusing on numerical algorithms [27]. The purpose of this paper is to fill these gaps, as we present constant-factor approximation algorithms the bin packing problem, both for U Ω and U Γ .…”

Section: Robust Bin Packing (Rbp)mentioning

confidence: 97%

Approximating Robust Bin Packing with Budgeted Uncertainty

Roy

Bougeret

Goldberg

et al. 2019

Lecture Notes in Computer Science

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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 U Γ 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 U Ω model, bounds the total amount of deviation in each scenario. We show that a variant of the next-fit algorithm is a 2 approximation for the U Ω model, and another variant of this algorithm is a 2Γ approximation for the U Γ model. This first result motivates the question of the existence of a constant approximation factor algorithm for the U Γ model. Our main result affirms this question by developing a dynamic-programming based algorithm for which a 3 + ρ ≤ 4.5 approximation factor is proven for the U Γ model, where ρ is an approximation factor guarantee of a classical bin packing approximation algorithm.

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“…Sticking to U Γ , the authors of [5] prove that the robust counterpart of 1|| C j with uncertain processing times is polynomially solvable. They further provide constant factor approximations algorithms for scheduling problems with parallel machines, later improved in [4]. The related bin-packing problem has also been investigated in [3], where the authors provide constant factor approximation algorithms.…”

Section: Introductionmentioning

confidence: 99%