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A 3/2-approximation for big two-bar charts packing

Author

Listed:
  • Adil Erzin

    (Sobolev Institute of Mathematics)

  • Georgii Melidi

    (Sobolev Institute of Mathematics)

  • Stepan Nazarenko

    (Sobolev Institute of Mathematics)

  • Roman Plotnikov

    (Sobolev Institute of Mathematics)

Abstract

We consider a Two-Bar Charts Packing Problem (2-BCPP), in which it is necessary to pack two-bar charts (2-BCs) in a unit-height strip of minimum length. The problem is a generalization of the Bin Packing Problem. Earlier, we proposed an $$O(n^2)$$ O ( n 2 ) –time algorithm that constructs the packing of n arbitrary 2-BCs, whose length is at most $$2\cdot OPT+1$$ 2 · O P T + 1 , where OPT is the minimum packing length. This paper proposes two new 3/2–approximate algorithms based on sequential matching. One has time complexity $$O(n^4)$$ O ( n 4 ) and is applicable when at least one bar of each 2-BC is greater than 1/2. Another has time complexity $$O(n^{3.5})$$ O ( n 3.5 ) and is applicable when, additionally, all BCs are non-increasing or non-decreasing. We prove the estimate’s tightness and conduct a simulation to compare the constructed packings with the optimal solutions or a lower bound of optimum.

Suggested Citation

  • Adil Erzin & Georgii Melidi & Stepan Nazarenko & Roman Plotnikov, 2021. "A 3/2-approximation for big two-bar charts packing," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 71-84, July.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:1:d:10.1007_s10878-021-00741-1
    DOI: 10.1007/s10878-021-00741-1
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    References listed on IDEAS

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    1. Kolisch, Rainer & Hartmann, Sonke, 2006. "Experimental investigation of heuristics for resource-constrained project scheduling: An update," European Journal of Operational Research, Elsevier, vol. 174(1), pages 23-37, October.
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