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}
}
  • K. Jansen, M. Rau
  • 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… 
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TLDR
A pseudo-polynomial algorithm with improved approximation ratio 4 / 3 + e .
Improved Pseudo-Polynomial-Time Approximation for Strip Packing
TLDR
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
TLDR
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 $\mathcal{P} \not= \mathcal {NP}$.
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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)).
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
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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 \(5}{4}\).
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