The Online Knapsack Problem with Departures

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.

Near-optimal Online Algorithms for Joint Pricing and Scheduling in EV Charging Networks

“…The online knapsack problem and its variants have been extensively studied in the literature [26,31,27,25,34,35]. Nearly all online algorithms in this stream of works are based on a similar idea that estimates the price of admitting one item using a function of the knapsack utilization and admits the item if item value is larger than the estimated price.…”

“…This paper designs an order-optimal online algorithm for the most general integral setting. Compared to the other two works with optimal CRs (i.e., [26] and [25]), this work makes additional technical contributions in design and analysis of the algorithm in the general setting. In particular, we extend the analysis of the fractional admission in [26] to integral admission by considering two classes of instances and analyzing their corresponding worst-case ratios using different approaches (see Section 4.2 and 4.3).…”

“…In particular, we extend the analysis of the fractional admission in [26] to integral admission by considering two classes of instances and analyzing their corresponding worst-case ratios using different approaches (see Section 4.2 and 4.3). We extend the fixed demand setting in [25] to scheduling setting by formulating an auxiliary cost minimization (see problem (2)) for scheduling decisions and analyzing the CR by an online primal-dual approach. Further, our primal-dual analysis results in a natural design of the pricing function, which is in contrast to the ad-hoc design in [25].…”

“…We extend the fixed demand setting in [25] to scheduling setting by formulating an auxiliary cost minimization (see problem (2)) for scheduling decisions and analyzing the CR by an online primal-dual approach. Further, our primal-dual analysis results in a natural design of the pricing function, which is in contrast to the ad-hoc design in [25]. In addition, this paper takes into account the resource cost, which adds an extra dimension in the algorithm analysis.…”

Optimal Mechanism in a Dynamic Stochastic Knapsack Environment

“…Notably, they suggested that the optimal allocation and pricing rules are threshold policies, which offer a uniform price to incoming buyers and the buyers either accept or reject the offer. Furthermore, various computation algorithms for DSKP have been developed to implement allocation policies in practical scenarios (Zhou, Chakrabarty, and Lukose 2008;Han, Kawase, and Makino 2015;Im et al 2021;Sun et al 2022). They focused on online algorithms to allocate resources in response to changing demands and constraints.…”