Two for One: Tight Approximation of 2D Bin Packing

Authors:
Klaus Jansen;Lars Prädel;Ulrich M. Schwarz
Affiliations:
Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany 24098;Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany 24098;Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Kiel, Germany 24098
Venue:
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Year:
2009

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Abstract

In this paper, we study the two-dimensional geometrical bin packing problem (2DBP): given a list of rectangles, provide a packing of all these into the smallest possible number of 1×1 bins without rotating the rectangles. We present a 2-approximate algorithm, which improves over the previous best known ratio of 3, matches the best results for the rotational case and also matches the known lower bound of approximability. Our approach makes strong use of a recently-discovered PTAS for a related knapsack problem and a new algorithm that can pack instances into OPT + 2 bins for any constant OPT.