Bin Packing with Multiple Colors

TL;DR

This paper introduces optimal, linear-time algorithms for the Colored Bin Packing problem with multiple colors, showing the problem remains tractable as the number of colors increases, for zero and unit weight items.

Contribution

The paper presents the first optimal linear-time algorithms for multi-color bin packing with zero and unit weights, demonstrating the problem's complexity does not increase with more colors.

Findings

Algorithms are optimal and run in linear time.

The problem remains tractable with multiple colors.

Closed-form expressions for the minimum number of bins are provided.

Abstract

In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the case where there are two or more colors when the items have zero weight and when the items have unit weight. Our algorithms are optimal and run in linear time. Since our algorithms apply for two or more colors, they demonstrate that the problem does not get harder as the number of colors increases. We also provide closed-form expressions for the optimal number of bins.