G\'lvez, Waldo and Grandoni, Fabrizio and Ingala, Salvatore and Khan, Arindam (2016) Improved Pseudo-Polynomial-Time Approximation for Strip Packing. In: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016, December 13-15, 2016, Chennai, India.
Full text not available from this repository.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 axis-parallel rectangles in the two-dimensional 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 non-overlapping 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 P6=NP). Nadiradze and Wiese [SODA16] overcame this barrier by presenting a (75 + ǫ)-approximation algorithm in pseudo-polynomial-time (PPT). As the problem is strongly NP-hard, it does not admit an exact PPT algorithm. In this paper we make further progress on the PPT approximability of strip packing, by presenting a (43 +ǫ)-approximation algorithm. Our result is based on a non-trivial 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◦, achieving the same approximation factor and breaking the polynomial-time approximation barrier of 3/2 for the case with rotations as well.
| Item Type: | Article in conference proceedings or Presentation at a conference (Paper) |
|---|---|
| Subjects: | Computer sciences > Computer science > Computational science foundations |
| Department/unit: | Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sull’intelligenza artificiale USI-SUPSI |
| Depositing User: | Fabrizio Grandoni |
| Date Deposited: | 17 Jul 2023 11:13 |
| Last Modified: | 17 Jul 2023 11:19 |
| URI: | http://repository.supsi.ch/id/eprint/14343 |
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