# Improved Online Algorithm for Fractional Knapsack in the Random Order Model

arXiv: https://arxiv.org/abs/2109.04428 · HTML: https://mlsanity.com/paper/2109.04428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2021.

## Built on by (most cited first, 1 of 1)

- [Near-Optimal Consistency-Robustness Trade-Offs for Learning-Augmented Online Knapsack Problems](https://mlsanity.com/paper/2406.18752/) (2024)

## Abstract (arXiv)

The fractional knapsack problem is one of the classical problems in combinatorial optimization, which is well understood in the offline setting. However, the corresponding online setting has been handled only briefly in the theoretical computer science literature so far, although it appears in several applications. Even the previously best known guarantee for the competitive ratio was worse than the best known for the integral problem in the popular random order model. We show that there is an algorithm for the online fractional knapsack problem that admits a competitive ratio of 4.39. Our result significantly improves over the previously best known competitive ratio of 9.37 and surpasses the current best 6.65-competitive algorithm for the integral case. Moreover, our algorithm is deterministic in contrast to the randomized algorithms achieving the results mentioned above.