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A 4/3 OPT+2/3 Approximation for Big Two-Bar Charts Packing Problem

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We consider the two-bar charts packing problem generalizing the strongly NP-hard bin packing problem. We prove that the problem remains strongly NP-hard even if each two-bar chart has at least one bar higher than 1/2. If the first (or second) bar of each two-bar chart is higher than 1/2, we show that the O(n2)-time greedy algorithm with lexicographic ordering of two-bar charts constructs a packing of length at most OPT+1, where OPT is optimum, and present an O(n2.5)-time algorithm that constructs a packing of length at most 4/3 ・ OPT+2/3 in the NP-hard case where each two-bar chart has at least one bar higher than 1/2.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr, Novosibirsk, 630090, Russia

    A. I. Erzin & A. V Kononov

  2. Sorbonne University, CNRS, Laboratoire d’informatique de Paris 6, Paris, France

    G. E. Melidi

  3. Novosibirsk State University, 1, Pirogova St, Novosibirsk, 630090, Russia

    S. A. Nazarenko

Authors
  1. A. I. Erzin
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  2. A. V Kononov
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  3. G. E. Melidi
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  4. S. A. Nazarenko
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Correspondence to A. I. Erzin.

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JMS Source Journal International Mathematical Schools. Vol. 2. Advances in Pure and Applied Mathematics

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Erzin, A.I., Kononov, A.V., Melidi, G.E. et al. A 4/3 OPT+2/3 Approximation for Big Two-Bar Charts Packing Problem. J Math Sci 269, 813–822 (2023). https://doi.org/10.1007/s10958-023-06319-y

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  • DOI: https://doi.org/10.1007/s10958-023-06319-y

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