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A note on the lower bound for online strip packing W. Kern and J.J. Paulus

Summary: A note on the lower bound for online strip packing
W. Kern and J.J. Paulus
This note presents a lower bound of 3/2+

33/6 2.457 on the competitive ratio
for online strip packing. The instance construction we use to obtain the lower bound
was first coined by Brown, Baker and Katseff [2]. Recently this instance construction
is used to improve the lower bound in computer aided proofs. We derive the best
possible lower bound that can be obtained with this instance construction.
1 Introduction
In the two-dimensional strip packing problem a number of rectangles have to be
packed without rotation or overlap into a strip such that the height of the strip
used is minimum. The width of the rectangles is bounded by 1 and the strip has
width 1 and infinite height. Baker, Coffman and Rivest [1] show that this problem
is NP-hard.
We study the online version of this packing problem. In the online version the
rectangles are given to the online algorithm one by one from a list, and the next
rectangle is given as soon as the current rectangle is irrevocably placed into the strip.
To evaluate the performance of an online algorithm we employ competitive analysis.


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering