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October 3, 2025Open Access

A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm

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New rectangle ordering enhances the Bottom-Left Algorithm, achieving a 13/6 approximation in strip packing, indicating significant advancement.

The Bottom-Left Algorithm reaches a 13/6 approximation ratio for Strip Packing with a novel rectangle ordering, a notable improvement.
Previous bounds showed a maximum approximation ratio of 3, established by sorting rectangles by width; this new approach represents a breakthrough.
The Strip Packing problem remains NP-hard, but efficient heuristics like our new approach offer comprehensive insights for practical applications.
For 45 years, no other ordering improved the Bottom-Left Algorithm's efficiency, underscoring the importance of this advancement in optimization techniques.

Hougardy et al. (2025) studied this question.

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New rectangle ordering enhances the Bottom-Left Algorithm, achieving a 13/6 approximation in strip packing, indicating significant advancement.