The Online Knapsack Problem with Departures

TL;DR

This paper extends the online knapsack problem to include item departures, multiple knapsacks, and multi-dimensional sizes, proposing algorithms with strong theoretical guarantees and practical performance improvements.

Contribution

It introduces a threshold-based online algorithm for the generalized problem and a data-driven approach that learns to optimize performance in typical instances.

Findings

The threshold-based algorithm achieves order-optimal competitive ratios.

The data-driven algorithm outperforms benchmarks in cloud job scheduling.

Proven worst-case performance bounds for the proposed algorithms.

Abstract

The online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack. In this paper, we study a general version that includes item departures, while also considering multiple knapsacks and multi-dimensional item sizes. We design a threshold-based online algorithm and prove that the algorithm can achieve order-optimal competitive ratios. Beyond worst-case performance guarantees, we also aim to achieve near-optimal average performance under typical instances. Towards this goal, we propose a data-driven online algorithm that learns within a policy-class that guarantees a worst-case performance bound. In trace-driven experiments, we show that our data-driven algorithm outperforms other benchmark algorithms in an application of online knapsack to job scheduling for cloud computing.