Colored Bin Packing

TL;DR

This paper introduces optimal linear-time algorithms for the Colored Bin Packing problem with zero and unit weights, focusing on minimizing bins while avoiding adjacent same-color items within each bin.

Contribution

It provides the first linear-time algorithms for the zero-weight and unit-weight versions of the colored bin packing problem, addressing a gap in existing solutions.

Findings

Linear-time optimal algorithms for zero-weight items

Linear-time optimal algorithms for unit-weight items

Efficient solutions for color adjacency constraints

Abstract

We study the Colored Bin Packing Problem: we are given a set of items where each item has a weight and color. We must pack the items in bins of uniform capacity such that no two items of the same color may be adjacent within in a bin. The goal is to perform this packing using the fewest number of bins. We consider a version of the problem where reordering is allowed. We first consider the zero-weight and unit weight versions of this problem, i.e. where the items have weight zero and one, respectively. We present linear time optimal algorithms for both versions.