Improved Online Algorithm for Fractional Knapsack in the Random Order Model

TL;DR

This paper presents a deterministic online algorithm for the fractional knapsack problem in the random order model, achieving a significantly improved competitive ratio of 4.39 over previous methods.

Contribution

It introduces the first deterministic algorithm with a competitive ratio of 4.39 for online fractional knapsack in the random order model, surpassing prior randomized approaches.

Findings

Achieved a competitive ratio of 4.39, better than previous 9.37.

Outperformed the best integral case with a 6.65 ratio.

Algorithm is deterministic, unlike earlier randomized algorithms.

Abstract

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.