Updated Estimates for Algorithms for Packing 2-Bar Charts in a Strip

We consider a two-bar charts packing problem in which it is necessary to pack bar chartsconsisting of two bars in a unit-height strip of minimum length. Each bar has a height of at most1 and unit length. The problem under consideration is NP-hard and generalizes the bin packingproblem and two-dimensional vector packing problem. This paper proves updated accuracyestimates and time complexity for several previously developed polynomial approximationalgorithms for the two-bar charts packing problem and particular cases of the problem. We showthe attainability of the estimates. Furthermore, we consider a problem of packing an unlimitednumber of bar charts belonging to \(k\) different types and propose a polynomial algorithm to solve the problem incase \(k = \text {const}\) .