# Improved Approximation for Two Dimensional Strip Packing with Polynomial Bounded Width

@inproceedings{Jansen2017ImprovedAF, title={Improved Approximation for Two Dimensional Strip Packing with Polynomial Bounded Width}, author={Klaus Jansen and Malin Rau}, booktitle={WALCOM}, year={2017} }

We study the well-known two-dimensional strip packing problem. Given is a set of rectangular axis-parallel items and a strip of width W with infinite height. The objective is to find a packing of these items into the strip, which minimizes the packing height. Lately, it has been shown that the lower bound of 3/2 of the absolute approximation ratio can be beaten when we allow a pseudo-polynomial running-time of type \((n W)^{f(1/\varepsilon )}\), for any function f. If W is polynomially bounded…

## 15 Citations

Improved approximation for two dimensional Strip Packing with polynomial bounded width

- Computer Science, MathematicsTheor. Comput. Sci.
- 2019

A pseudo-polynomial algorithm with improved approximation ratio 4 / 3 + e .

Improved Pseudo-Polynomial-Time Approximation for Strip Packing

- Mathematics, Computer ScienceFSTTCS
- 2016

Their PPT algorithm can be adapted to the case where the authors are allowed to rotate the rectangles by $90^\circ$, achieving the same approximation factor and breaking the polynomial-time approximation barrier of 3/2 for the case with rotations as well.

High Multiplicity Strip Packing Problem With Three Rectangle Types

- Mathematics
- 2019

The two-dimensional strip packing problem (2D-SPP) involves packing a set R = {r1, ..., rn} of n rectangular items into a strip of width 1 and unbounded height, where each rectangular item ri has…

Hardness of Approximation for Strip Packing

- Mathematics, Computer ScienceTOCT
- 2017

This article proves that it is NP-hard to approximate strip packing within a factor better than 12/11, even when restricted to polynomially bounded input data, and shows that the strip packing problem admits no quasi-polynomial time approximation scheme, unless NP} ⊑ DTIME(2polylog (n)).

A Tight (3/2+ε) Approximation for Skewed Strip Packing

- Computer Science, MathematicsAPPROX-RANDOM
- 2020

This work considers the complementary case where all the rectangles are skewed and provides an (almost) tight (3/2 + ε)-approximation algorithm for Strip Packing.

Linear Time Algorithms for Multiple Cluster Scheduling and Multiple Strip Packing

- Computer Science, MathematicsEuro-Par
- 2019

This paper presents an algorithm with approximation ratio $2$ and running time $O(n)$ for both problems and points out that the general approach of finding first a schedule on one cluster and then distributing it onto the other clusters might come in handy in practical approaches.

Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

- Mathematics, Computer ScienceTheory of Computing Systems
- 2019

A positive answer to the long-standing open question whether this problem is strongly NP-complete for m = 4 is given, and the lower bound of 12 11 $\frac {12}{11}$ is improved for approximating pseudo-polynomial Strip Packing to 5 4 $\frac{5}{4}$ .

Approximation Algorithms for Demand Strip Packing

- Computer ScienceAPPROX-RANDOM
- 2021

The main result is a (5/3 + ε)approximation algorithm for any constant ε > 0.5, which achieves best-possible approximation factors for some relevant special cases.

Approximation and online algorithms for multidimensional bin packing: A survey

- Computer ScienceComput. Sci. Rev.
- 2017

This survey considers approximation and online algorithms for several classical generalizations of bin packing problem such as geometric bin packing, vector bin packing and various other related problems.

Approximating Geometric Knapsack via L-Packings

- Mathematics, Computer Science2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

This paper breaks the 2 approximation barrier, achieving a polynomialtime 17/9 + ε and aims to find a (non-overlapping) packing of a maximum profit subset of items inside the knapsack.

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Improved approximation for two dimensional Strip Packing with polynomial bounded width

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A pseudo-polynomial algorithm with improved approximation ratio 4 / 3 + e .

Improved Pseudo-Polynomial-Time Approximation for Strip Packing

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Their PPT algorithm can be adapted to the case where the authors are allowed to rotate the rectangles by $90^\circ$, achieving the same approximation factor and breaking the polynomial-time approximation barrier of 3/2 for the case with rotations as well.

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This article proves that it is NP-hard to approximate strip packing within a factor better than 12/11, even when restricted to polynomially bounded input data, and shows that the strip packing problem admits no quasi-polynomial time approximation scheme, unless NP} ⊑ DTIME(2polylog (n)).

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