Tight Approximation Algorithms for Two-Dimensional Guillotine Strip Packing
In the Strip Packing problem (SP), we are given a vertical half-strip [0,W]×[0,∞) and a set of n axis-aligned rectangles of width at most W. The goal is to find a non-overlapping packing of all rectangles into the strip such that the height of the packing is minimized. A well-studied and frequently used practical constraint is to allow only those packings that are guillotine separable, i.e., every rectangle in the packing can be obtained by recursively applying a sequence of edge-to-edge axis-parallel cuts (guillotine cuts) that do not intersect any item of the solution. In this paper, we study approximation algorithms for the Guillotine Strip Packing problem (GSP), i.e., the Strip Packing problem where we require additionally that the packing needs to be guillotine separable. This problem generalizes the classical Bin Packing problem and also makespan minimization on identical machines, and thus it is already strongly NP-hard. Moreover, due to a reduction from the Partition problem, it is NP-hard to obtain a polynomial-time (3/2-ε)-approximation algorithm for GSP for any ε > 0 (exactly as Strip Packing). We provide a matching polynomial time (3/2+ε)-approximation algorithm for GSP. Furthermore, we present a pseudo-polynomial time (1+ε)-approximation algorithm for GSP. This is surprising as it is NP-hard to obtain a (5/4-ε)-approximation algorithm for (general) Strip Packing in pseudo-polynomial time. Thus, our results essentially settle the approximability of GSP for both the polynomial and the pseudo-polynomial settings.
Approximation Algorithms
Two-Dimensional Packing
Rectangle Packing
Guillotine Cuts
Computational Geometry
Theory of computation~Design and analysis of algorithms
80:1-80:20
Track A: Algorithms, Complexity and Games
https://arxiv.org/pdf/2202.05989.pdf
A part of this work was done when Arnab Maiti and Amatya Sharma were undergraduate interns at Indian Institute of Science.
Arindam
Khan
Arindam Khan
Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India
https://www.csa.iisc.ac.in/~arindamkhan/
https://orcid.org/0000-0001-7505-1687
Arindam Khan was supported in part by Pratiksha Trust Young Investigator Award, Google CSExplore Award, and Google India Research Award.
Aditya
Lonkar
Aditya Lonkar
Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India
http://www.myhomepage.edu
Arnab
Maiti
Arnab Maiti
Indian Institute of Technology, Kharagpur, India
https://sites.google.com/view/arnab-maiti/home
Amatya
Sharma
Amatya Sharma
Indian Institute of Technology, Kharagpur, India
https://aaysharma.github.io
Andreas
Wiese
Andreas Wiese
Technische Universität München, Germany
https://discrete.ma.tum.de/people/professors/andreas-wiese.html
https://orcid.org/0000-0003-3705-016X
Andreas Wiese was partially supported by the Fondecyt Regular grant 1200173.
10.4230/LIPIcs.ICALP.2022.80
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Arindam Khan, Aditya Lonkar, Arnab Maiti, Amatya Sharma, and Andreas Wiese
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