2026-07-20T11:16:36Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6844 2024-03-06T10:39:01Z ddc:004 open_access

Improved Pseudo-Polynomial-Time Approximation for Strip Packing Gálvez, Waldo Grandoni, Fabrizio Ingala, Salvatore Khan, Arindam approximation algorithms strip packing rectangle packing cutting-stock problem 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 P!=NP). Nadiradze and Wiese [SODA16] overcame this barrier by presenting a (7/5+epsilon)-approximation algorithm in pseudo-polynomial-time (PPT). As the problem is strongly NP-hard, 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 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 degrees, achieving the same approximation factor and breaking the polynomial-time approximation barrier of 3/2 for the case with rotations as well. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Waldo Gálvez and Fabrizio Grandoni and Salvatore Ingala and Arindam Khan 2016 Is Part Of LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2016.9 urn:nbn:de:0030-drops-68445 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.9 eng https://creativecommons.org/licenses/by/3.0/legalcode