Elsevier

Theoretical Computer Science

Volume 789, 15 October 2019, Pages 34-49
Theoretical Computer Science

Improved approximation for two dimensional Strip Packing with polynomial bounded width

https://doi.org/10.1016/j.tcs.2019.04.002Get rights and content
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Abstract

We study the well-known two-dimensional Strip Packing problem. Given a set of rectangular axis-parallel items and a strip of width W with infinite height, the objective is to find a packing of all 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 (nW)f(1/ε). If W is polynomially bounded by the number of items, this is a polynomial running-time. The currently best pseudo-polynomial approximation algorithm by Nadiradze and Wiese achieves an approximation ratio of 1.4+ε. We present a pseudo-polynomial algorithm with improved approximation ratio 4/3+ε. Furthermore, the presented algorithm has a significantly smaller running-time as the 1.4+ε approximation algorithm.

Keywords

Strip Packing
Pseudo polynomial
Structural Lemma
Approximation Algorithm

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Research was supported in part by German Research Foundation (DFG) project JA 612 /14-2. An extended abstract of this paper was published at WALCOM 2017 [9].