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

Adil Erzin (), Georgii Melidi, Stepan Nazarenko and Roman Plotnikov
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Adil Erzin: Sobolev Institute of Mathematics
Georgii Melidi: Sobolev Institute of Mathematics
Stepan Nazarenko: Sobolev Institute of Mathematics
Roman Plotnikov: Sobolev Institute of Mathematics

Journal of Combinatorial Optimization, 2021, vol. 42, issue 1, No 5, 84 pages

Abstract: 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.

Keywords: Bar Charts; Strip Packing; Approximation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10878-021-00741-1

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