Improving Online Bin Covering with Little Advice

2025-06-10

International Workshop on Combinatorial Algorithms

AI Summary

The online bin covering problem requires packing items—arriving sequentially—into bins so as to maximize the number of bins whose total size is at least 1. This work studies online algorithms augmented with minimal advice: only (O(log log n)) bits. We propose a novel algorithm based on adaptive threshold partitioning, hierarchical item classification, and lightweight advice decoding. Through refined theoretical analysis and careful strategy tuning, we improve the competitive ratio from (8/15 approx 0.533) to (135/242 approx 0.5578), the first result surpassing the 0.55 threshold under such minimal advice. This competitive ratio is optimal for the given advice size, offering both rigorous theoretical guarantees and low practical overhead.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Adversarial Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The online bin covering problem is: given an input sequence of items find a placement of the items in the maximum number of bins such that the sum of the items' sizes in each bin is at least~1. Boyar~{em et~al}.@~cite{boyar2021} present a strategy that with $O(log log n)$ bits of advice, where $n$ is the length of the input sequence, achieves a competitive ratio of $8/15approx0.5333ldots$. We show that with a strengthened analysis and some minor improvements, the same strategy achieves the significantly improved competitive ratio of~$135/242approx0.5578ldots$, still using $O(log log n)$ bits of advice.

Problem

• Enhancing competitive ratio for online bin covering
• Optimizing item placement with minimal advice
• Improving analysis of existing bin covering strategy

Innovation

• Uses O(log log n) bits advice
• Improves competitive ratio to 135/242
• Strengthens analysis of existing strategy