Khan, A and Lonkar, A and Maiti, A and Sharma, A and Wiese, A
(2022)
*Tight Approximation Algorithms for Two-Dimensional Guillotine Strip Packing.*
In: 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022, 4 - 8 July 2022, Paris.

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## Abstract

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.

Item Type: | Conference Paper |
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Publication: | Leibniz International Proceedings in Informatics, LIPIcs |

Publisher: | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Additional Information: | The copyright for this article belongs to the Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. |

Keywords: | Computational geometry; Polynomial approximation, Edge-to-edge; Guillotine cuts; NP-hard; Parallel cuts; Polynomial-time; Rectangle packing; Strip packing; Strip packing problem; Two-dimensional; Two-dimensional packing, Approximation algorithms |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 20 Jul 2022 12:05 |

Last Modified: | 20 Jul 2022 12:05 |

URI: | https://eprints.iisc.ac.in/id/eprint/74943 |

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