# Fast Approximation Schemes for Bin Packing

## TL;DR

This paper introduces new approximation schemes for bin packing that leverage problem partitioning and irregular bin sizes to develop efficient recursive algorithms with improved approximation guarantees.

## Contribution

It proposes novel approximation schemes based on problem partitioning and irregular bin sizes, enhancing efficiency and solution quality for bin packing.

## Key findings

- Effective recursive algorithms for bin packing
- Improved approximation ratios achieved
- Flexible approach for different bin sizes

## Abstract

We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of these constant size sub-problems obtained through PTAS or exact methods; (2) solving bin packing using irregular sized bins, a generalization of bin packing, that facilitates the design of simple and efficient recursive algorithms that solve a problem in terms of smaller sub-problems such that the unused space in bins used by an earlier solved sub-problem is available to subsequently solved sub-problems.