# Multidimensional Bin Packing and Other Related Problems : A Survey ∗

@inproceedings{Christensen2016MultidimensionalBP, title={Multidimensional Bin Packing and Other Related Problems : A Survey ∗}, author={Henrik I. Christensen and A. Khan and Sebastian Pokutta and Prasad Tetali}, year={2016} }

The bin packing problem is a well-studied problem in combinatorial optimization. In the classical bin packing problem, we are given a list of real numbers in (0, 1] and the goal is to place them in a minimum number of bins so that no bin holds numbers summing to more than 1. The problem is extremely important in practice and finds numerous applications in scheduling, routing and resource allocation problems. Theoretically the problem has rich connections with discrepancy theory, iterative…

## 16 Citations

### Online bin packing of squares and cubes

- Computer Science, MathematicsWADS
- 2021

Improved upper bounds on the asymptotic competitive ratio forsquare and cube bin packing problems, where the authors' bounds do not exceed 2.0885 and 2.5735 for square and cube packing, respectively are provided.

### Solving the Batch Stochastic Bin Packing Problem in Cloud: A Chance-constrained Optimization Approach

- Computer ScienceKDD
- 2022

A new objective metric, Used Capacity at Confidence (UCaC), is defined, which measures the maximum used resources at a probability and is proved to be consistent for both empty and nonempty machines and reformulate the SBPP under chance constraints.

### Approximation Algorithms for Scheduling with Class Constraints

- Computer ScienceSPAA
- 2020

It is proved that there always exists an optimal solution where the jobs are split evenly and the number of pieces for each job is bounded, and these job pieces will be placed in just a few specific positions.

### Online Adaptive Bin Packing with Overflow

- Computer ScienceArXiv
- 2020

This work presents an online algorithm with expected cost at most a constant factor times the cost incurred by the optimal packing policy when item sizes are drawn from an i.i.d. sequence of unknown length and gives a similar result when item size distributions are exponential with arbitrary rates.

### Discovering Action Regions for Solving the Bin Packing Problem through Hyper-heuristics

- Computer Science, Business2020 IEEE Symposium Series on Computational Intelligence (SSCI)
- 2020

This work proposes a solution model that incorporates insights from unsupervised learning to produce solvers that base their decisions on maximizing a reward, and takes the form of a hyper-heuristic.

### Sharing-Aware Online Virtual Machine Packing in Heterogeneous Resource Clouds

- Computer ScienceIEEE Transactions on Parallel and Distributed Systems
- 2017

The experimental results show that the proposed sharing-aware online algorithms activate a smaller average number of physical servers relative to the sharing-oblivious algorithms, directly reduce the amount of required memory, and thus, require fewer physical servers to instantiate the VM instances requested by users.

### Smart Pack: Online Autonomous Object-Packing System Using RGB-D Sensor Data

- Computer ScienceSensors
- 2020

A novel online object-packing system which can measure the dimensions of every incoming object and calculate its desired position in a given container and the experimental results show that the proposed system successfully places the incoming various shaped objects in their proper positions.

### Efficient Data Allocation Heuristics for Data Center Server Consolidation

- Computer Science
- 2018

This paper investigates the data allocation for server consolidation in a data center to minimize the number of active servers using a recently developed technique of Vector Bin Packing and proposes both offline and online heuristic algorithms.

### Scheduling Distributed Resources in Heterogeneous Private Clouds

- Computer Science2018 IEEE 26th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS)
- 2018

This paper considers the static problem of allocating resources to multiple distributed application frameworks, possibly with different priorities and server preferences, in a private cloud with heterogeneous servers and considers the online problem by implementing variants of these schedulers in Apache Mesos using progressive filling to dynamically approximate max-min fair allocations.

### Stochastic Models for Resource Allocation in Large Distributed Systems. (Modèles Stochastiques pour l'Allocation des Ressources dans les Grands Systèmes Distribués)

- Computer Science
- 2017

This PhD thesis investigates four problems in the context of Large Distributed Systems, investigating the efficiency of different resource allocation algorithms in this framework through a mathematical analysis of several stochastic models associated to these networks.

## References

SHOWING 1-10 OF 176 REFERENCES

### On Multidimensional Packing Problems

- BusinessSIAM J. Comput.
- 2004

Packing integer programs capture a core problem that directly relates to both vector scheduling and vector bin packing, namely, the problem of packing a maximum number of vectors in a single bin of unit height.

### Two-dimensional bin packing with one-dimensional resource augmentation

- MathematicsDiscret. Optim.
- 2007

### A branch-and-bound algorithm for the two-dimensional vector packing problem

- Computer Science, BusinessComput. Oper. Res.
- 1994

### Lower bounds and algorithms for the 2-dimensional vector packing problem

- Computer ScienceDiscret. Appl. Math.
- 2001

### Approximation Algorithms for Bin Packing Problems: A Survey

- Computer Science
- 1981

This work surveys the approximation results that have been obtained for the classical one-dimensional bin packing problem and its many variants and generalizations, including recent (unpublished) work that reflects the currently most active areas of bin packing research.

### A tale of two dimensional bin packing

- Mathematics46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- 2005

This work studies the case of 'orthogonal packing without rotations', where rectangles cannot be rotated and must be packed parallel to the edges of a bin, and admits an asymptotic polynomial time approximation scheme.

### Multiple-type, two-dimensional bin packing problems: Applications and algorithms

- Business, Computer ScienceAnn. Oper. Res.
- 1994

Three solution algorithms have been developed and tested: a simple greedy heuristic, a method based on simulated annealing (SA), and an exact algorithm based onColumn Generation with Branch and Bound (CG), an LP-based method for generating tight lower bounds was also developed (LB).

### Online Stochastic Bin Packing

- Computer ScienceArXiv
- 2012

Two distribution-agnostic bin packing heuristics are presented that achieve additive O(sqrt{n}) waste compared to OPT for all distributions and the Best Fit heuristic is briefly revisited.

### Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem

- BusinessINFORMS J. Comput.
- 2007

This work proposes an algorithm based on the well-known Dantzig-Wolfe decomposition where the master problem deals with the production constraints on the rectangles while the subproblem deal with the packing of rectangles into a single bin and generates valid inequalities in a branch-and-cut system.

### Lower bounds for on-line two-dimensional packing algorithms

- Business, Computer ScienceActa Informatica
- 2004

Lower bounds for the worst-case performance of on-line algorithms for both non-preordered lists and for lists preordered by increasing or decreasing height or width are examined.