# 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}
}
• Published 18 June 2020
• J. Comb. Optim.
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…

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

ArXiv
• 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

• 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

Frontiers 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

Journal 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.

## References

SHOWING 1-10 OF 21 REFERENCES

### Two-Bar Charts Packing Problem

Optim. Lett.
• 2021
The algorithm proposed constructs a package in polynomial time, the length of which does not exceed $2\ OPT+1$, where $OPT$ is the minimum possible length of the packing and is the first guaranteed estimate for 2-BCPP.

### The Tight Bound of First Fit Decreasing Bin-Packing Algorithm Is FFD(I) <= 11/9OPT(I) + 6/9

It is shown in this paper that the tight bound of the additive constant was an open question for many years and that this bound is tight.

### A simple proof of the inequality MFFD(L)≤71/60 OPT(L) + 1,L for the MFFD bin-packing algorithm

• Mathematics
• 1991
In 1985, Johnson and Garey[4] devised an algorithm which they call MFFD. Compared with other modifications of the famous FFD algorithm, their is apparently simpler in practical applications and

### An o(n2.5) Algorithm: For Maximum Matchings in General Graphs

This article provides a new approach to deal with the blossom in alternating paths in the process of searching for augmenting paths, which different from well-known “shrinking” way of Edmonds and makes the algorithm for maximum matchings in general graphs more simple.

### Data structures for weighted matching and nearest common ancestors with linking

• H. Gabow
• Computer Science, Mathematics
SODA '90
• 1990
This paper shows that the weighted matching problem on general graphs can be solved in time O(n(m + n log n)), f or n and m the number of vertices and edges, respectively. This was previously known