Offline green bin packing and its constrained variant

2026-02-18

AI Summary

This study addresses the offline Green Bin Packing problem (GBP) and its constrained variant (CGBP), which jointly optimize the number of bins used and total energy consumption: GBP minimizes a weighted sum of these two objectives, while CGBP minimizes bin count subject to an energy consumption upper bound. The authors present the first asymptotic polynomial-time approximation scheme (APTAS) for both problems and introduce a combinatorial algorithm achieving a 3/2 approximation ratio—theoretical lower bound known for classical bin packing. By unifying the treatment of this bi-objective optimization setting, the work matches the best-known theoretical guarantees and establishes a novel algorithmic framework for green resource scheduling.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Efficient ML / Green AI

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

In this paper, we study the {\em green bin packing} (GBP) problem where $β\ge 0$ and $G \in [0, 1]$ are two given values as part of the input. The energy consumed by a bin is $\max \{0, β(x-G) \}$ where $x$ is the total size of the items packed into the bin. The GBP aims to pack all items into a set of unit-capacity bins so that the number of bins used plus the total energy consumption is minimized. When $β= 0$ or $G = 1$, GBP is reduced to the classic bin packing (BP) problem. In the {\em constrained green bin packing} (CGBP) problem, the objective is to minimize the number of bins used to pack all items while the total energy consumption does not exceed a given upper bound $U$. We present an APTAS and a $\frac 32$-approximation algorithm for both GBP and CGBP, where the ratio $\frac 32$ matches the lower bound of BP. Keywords: Green bin packing; constrained green bin packing; approximation scheme; offline algorithms

Problem

• Green bin packing
• Constrained green bin packing
• Bin packing
• Energy consumption
• Offline algorithms

Innovation

• green bin packing
• constrained green bin packing
• APTAS
• approximation algorithm
• offline algorithms