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

@article{Erzin2021A3F, title={A 3/2-approximation for big two-bar charts packing}, author={Adil I. Erzin and Stepan Nazarenko and Gregory Melidi and Roman V. Plotnikov}, journal={J. Comb. Optim.}, year={2021}, volume={42}, pages={71-84} }

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 (BPP). Earlier, we proposed an $O(n^2)$-time algorithm that constructs the packing which length at most $2\cdot OPT+1$, where $OPT$ is the minimum length of the packing of $n$ 2-BCs. In this paper, we propose an $O(n^4)$-time 3/2-approximate algorithm when each BC has at least one bar…

## 5 Citations

### Approximation Algorithms for Two-Bar Charts Packing Problem

- BusinessArXiv
- 2021

To construct the optimal solutions or lower bounds for optimum, the Boolean Linear Programming (BLP) formulation of 2-BCPP is used and the CPLEX package is applied and a database of instances for BPP with known optimal solutions is used to construct the instances for the 2- BCPP withknown minimal packing length.

### Mathematical models and decomposition methods for the two-bar charts packing problem

- Business
- 2022

We consider the two-bar charts packing (2-BCPP), a recent combinatorial optimization problem whose aim is to pack a set of one-dimensional items into the minimum number of bins. As opposed to the…

### Two-dimensional irregular packing problems: A review

- BusinessFrontiers in Mechanical Engineering
- 2022

Two-dimensional (2D) irregular packing problems are widespread in manufacturing industries such as shipbuilding, metalworking, automotive production, aerospace, clothing and furniture manufacturing.…

### An Improved Approximation for Packing Big Two-Bar Charts

- BusinessJournal of Mathematical Sciences
- 2022

This paper proposes an O(n)–time 16/11–approximation algorithm for packing 2-BCs when at least one bar of each BC has a height not less than 1/2 and an O-time 5/4–app approximation algorithm forpacking nonincreasing or non-decreasing 2- BCs when each2-BC has at leastOne bar which height is more than1/2.

### A Posteriori Analysis of the Algorithms for Two-Bar Charts Packing Problem

- BusinessCommunications in Computer and Information Science
- 2021

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