# 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}
}
• Published in WALCOM 14 October 2016
• Mathematics, Computer Science
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

## Figures and Topics from this paper

Improved approximation for two dimensional Strip Packing with polynomial bounded width
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2019
A pseudo-polynomial algorithm with improved approximation ratio 4 / 3 + e .
Improved Pseudo-Polynomial-Time Approximation for Strip Packing
• Mathematics, Computer Science
FSTTCS
• 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
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 Science
TOCT
• 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, Mathematics
APPROX-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, Mathematics
Euro-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 Science
Theory 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 Science
APPROX-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 Science
Comput. 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 Science
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
• 2017
This paper breaks the 2 approximation barrier, achieving a polynomialtime 17/9 + &#x03B5; and aims to find a (non-overlapping) packing of a maximum profit subset of items inside the knapsack.

## References

SHOWING 1-10 OF 19 REFERENCES
Improved approximation for two dimensional Strip Packing with polynomial bounded width
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2019
A pseudo-polynomial algorithm with improved approximation ratio 4 / 3 + e .
Improved Pseudo-Polynomial-Time Approximation for Strip Packing
• Mathematics, Computer Science
FSTTCS
• 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.
Improved Absolute Approximation Ratios for Two-Dimensional Packing Problems
• Mathematics, Computer Science
APPROX-RANDOM
• 2009
This work presents a polynomial time approximation scheme for strip packing where rotations by 90 degrees are permitted and an algorithm for two-dimensional bin packing with an absolute worst-case ratio of 2, which is optimal provided $\mathcal{P} \not= \mathcal {NP}$.
On approximating strip packing with a better ratio than 3/2
• Computer Science, Mathematics
SODA
• 2016
This paper presents a (1.4 + e)-approximation algorithm with pseudo-polynomial running time that implies that for polynomially bounded input data the problem can be approximated with a strictly better ratio than for exponential input which is a very rare phenomenon in combinatorial optimization.
Hardness of Approximation for Strip Packing
• Mathematics, Computer Science
TOCT
• 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)).
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
• Mathematics, Computer Science
CSR
• 2018
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 $$\frac{12}{11}$$ for approximating pseudo-polynomial Strip Packing to $$5}{4}$$.
A 5/4 Algorithm for Two-Dimensional Packing
• Mathematics, Computer Science
J. Algorithms
• 1981
The ratio of the height obtained by the algorithm and the height used by an optimal packing is asymptotically bounded by 5 4, which is an improvement over the bound of 4 3 achieved by the best previous algorithm.
Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms
• Mathematics, Computer Science
SIAM J. Comput.
• 1980
This work analyzes several “level-oriented” algorithms for packing rectangles into a unit-width, infinite-height bin and gives more refined bounds for special cases in which the widths of the given rectangles are restricted and in which only squares are to be packed.
A (5/3 + ε)-Approximation for Strip Packing
• Mathematics, Computer Science