Improved Approximation for Vector Bin Packing

Bansal, Nikhil; Eliáš, Marek; Khan, Arindam

doi:10.1137/1.9781611974331.ch106

Cited by 40 publications

(63 citation statements)

References 24 publications

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“…For VECTOR BIN PACKING, we design a streaming asymptotic d + ε-approximation algorithm running in space O d ε · log d ε · log OPT ; see Section 3.3. We remark that if vectors are rounded into a sublinear number of types, then better than d-approximation is not possible [7].…”

Section: Our Resultsmentioning

confidence: 99%

“…VECTOR BIN PACKING proves to be substantially harder to approximate, even in a constant dimension. For fixed d, Bansal, Eliáš, and Khan [7] showed an approximation factor of ≈ 0.807+ln(d+1)+ε. For general d, a relatively simple algorithm based on an LP relaxation, due to Chekuri and Khanna [11], remains the best known, with an approximation guarantee of 1 + εd + O(log 1 ε ).…”

Section: Bin Packingmentioning

confidence: 98%

“…Implied by the proof of Theorem 2.2 in[7]). Any algorithm for VECTOR BIN PACKING that rounds up large coordinates of vectors to o(N/d) types cannot achieve better than d-approximation, where N is the number of vectors.It is an interesting open question whether or not we can design a streaming d + ε-approximation with o( d ε ) memory or even with O d + 1 ε memory.…”

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confidence: 99%

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Streaming Algorithms for Bin Packing and Vector Scheduling

Cormode

Veselý

2020

Lecture Notes in Computer Science

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Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases, but have been less well-studied when the volume of the input is truly massive, and cannot even be read into memory. This is captured by the streaming model of computation, where the aim is to approximate the cost of the solution in one pass over the data, using small space. As a result, streaming algorithms produce concise input summaries that approximately preserve the optimum value.We design the first efficient streaming algorithms for these fundamental problems in combinatorial optimization. For BIN PACKING, we provide a streaming asymptotic 1 + ε-approximation with O 1 ε memory, where O hides logarithmic factors. Moreover, such a space bound is essentially optimal. Our algorithm implies a streaming d + ε-approximation for VECTOR BIN PACKING in d dimensions, running in space O d ε . For the related VECTOR SCHEDULING problem, we show how to construct an input summary in space O(d 2 · m/ε 2 ) that preserves the optimum value up to a factor of 2 − 1 m + ε, where m is the number of identical machines.

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Section: Our Resultsmentioning

confidence: 99%

Section: Bin Packingmentioning

confidence: 98%

mentioning

confidence: 99%

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Streaming Algorithms for Bin Packing and Vector Scheduling

Cormode

Veselý

2020

Lecture Notes in Computer Science

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“…On the other hand, [6], using ideas from [17], showed that a d 1− -approximation would imply N P = ZP P . For fixed d (i.e., super-polynomial in d running times), the approximation factor improves to ln d + O(1) [9,8,16]. To overcome the strong lower bound for arbitrary d, Epstein [18] initiated the study of VBP with variable bin sizes.…”

Section: Online Vector Bin Packing (Vbp)mentioning

confidence: 99%

Randomized Algorithms for Online Vector Load Balancing

Azar¹,

Cohen²,

Panigrahi³

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study randomized algorithms for the online vector bin packing and vector scheduling problems. For vector bin packing, we achieve a competitive ratio ofÕ(d 1/B ), where d is the number of dimensions and B the size of a bin. This improves the previous bound ofÕ(d 1/(B−1) ) by a polynomial factor, and is tight up to logarithmic factors. For vector scheduling, we show a lower bound of Ω( log d log log d ) on the competitive ratio of randomized algorithms, which is the first result for randomized algorithms and is asymptotically tight. Finally, we analyze the widely used "power of two choices' algorithm for vector scheduling, and show that its competitive ratio is O(log log n + log d log log d ), which is optimal up to the additive O(log log n) term that also appears in the scalar version of this algorithm.

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“…The memory management problem is a typical 1D bin packing problem [2]. Unlike the multidimension bin packing problem whose dimensions have dependency on the others, the vector bin pack packing has a vector of independent dimensions [3]. The cluster resource management is a typical application in this domain.…”

Section: A Bin Packing Classificationmentioning

confidence: 99%

Small Boxes Big Data: A Deep Learning Approach to Optimize Variable Sized Bin Packing

Mao

Blanco²,

et al. 2017

2017 IEEE Third International Conference on Big Data Computing Service and Applications (BigDataService)

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Abstract-Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different variations and many heuristics have been proposed for obtaining approximate solutions. Specifically, for the 1D variable sized bin packing problem, the two key sets of optimization heuristics are the bin assignment and the bin allocation. Usually the performance of a single static optimization heuristic can not beat that of a dynamic one which is tailored for each bin packing instance. Building such an adaptive system requires modeling the relationship between bin features and packing perform profiles. The primary drawbacks of traditional AI machine learnings for this task are the natural limitations of feature engineering, such as the curse of dimensionality and feature selection quality. We introduce a deep learning approach to overcome the drawbacks by applying a large training data set, auto feature selection and fast, accurate labeling. We show in this paper how to build such a system by both theoretical formulation and engineering practices. Our prediction system achieves up to 89% training accuracy and 72% validation accuracy to select the best heuristic that can generate a better quality bin packing solution.

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Improved Approximation for Vector Bin Packing

Cited by 40 publications

References 24 publications

Streaming Algorithms for Bin Packing and Vector Scheduling

Streaming Algorithms for Bin Packing and Vector Scheduling

Randomized Algorithms for Online Vector Load Balancing

Small Boxes Big Data: A Deep Learning Approach to Optimize Variable Sized Bin Packing

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