Gálvez, Waldo ;
Grandoni, Fabrizio ;
Ingala, Salvatore ;
Khan, Arindam
Improved PseudoPolynomialTime Approximation for Strip Packing
Abstract
We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axisparallel rectangles in the twodimensional plane and the goal is to pack them in a vertical strip of fixed width such that the height of the obtained packing is minimized. The packing must be nonoverlapping and the rectangles cannot be rotated.
A reduction from the partition problem shows that no approximation better than 3/2 is possible for strip packing in polynomial time (assuming P!=NP). Nadiradze and Wiese [SODA16] overcame this barrier by presenting a (7/5+epsilon)approximation algorithm in pseudopolynomialtime (PPT). As the problem is strongly NPhard, it does not admit an exact PPT algorithm (though a PPT approximation scheme might exist).
In this paper we make further progress on the PPT approximability of strip packing, by presenting a (4/3+epsilon)approximation algorithm. Our result is based on a nontrivial repacking of some rectangles in the "empty space" left by the construction by Nadiradze and Wiese, and in some sense pushes their approach to its limit.
Our PPT algorithm can be adapted to the case where we are allowed to rotate the rectangles by 90 degrees, achieving the same approximation factor and breaking the polynomialtime approximation barrier of 3/2 for the case with rotations as well.
BibTeX  Entry
@InProceedings{glvez_et_al:LIPIcs:2016:6844,
author = {Waldo G{\'a}lvez and Fabrizio Grandoni and Salvatore Ingala and Arindam Khan},
title = {{Improved PseudoPolynomialTime Approximation for Strip Packing}},
booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
pages = {9:19:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770279},
ISSN = {18688969},
year = {2016},
volume = {65},
editor = {Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6844},
URN = {urn:nbn:de:0030drops68445},
doi = {10.4230/LIPIcs.FSTTCS.2016.9},
annote = {Keywords: approximation algorithms, strip packing, rectangle packing, cuttingstock problem}
}
2016
Keywords: 

approximation algorithms, strip packing, rectangle packing, cuttingstock problem 
Seminar: 

36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Issue date: 

2016 
Date of publication: 

2016 