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

TL;DR

This paper introduces a 3/2-approximation algorithm for the Two-Bar Charts Packing Problem, improving packing efficiency for charts with at least one bar exceeding half the strip's height.

Contribution

It presents a novel 3/2-approximate algorithm with polynomial time complexity for a generalized bin packing problem involving two-bar charts.

Findings

Achieves a 3/2 approximation ratio for the problem

Provides an algorithm with O(n^4) time complexity

Extends previous work with improved approximation bounds

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 (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 greater than 1/2.