Approximation Algorithms for Scheduling Crowdsourcing Tasks in Mobile Social Networks

Abstract: This paper addresses the scheduling problem in mobile social networks. We begin by proving that the approximation ratio analysis presented in the paper by Zhang \textit{et al.} (IEEE Transactions on Mobile Computing, 2025) is incorrect, and we provide the correct analysis results. Furthermore, when the required service time for a task exceeds the total contact time between the requester and the crowd worker, we demonstrate that the approximation ratio of the Largest-Ratio-First task scheduling algorithm can reach $2 - \frac{1}{m}$. Next, we introduce a randomized approximation algorithm to minimize mobile social networks' total weighted completion time. This algorithm achieves an expected approximation ratio of $1.5 + \epsilon$ for $\epsilon>0$. Finally, we present a deterministic approximation algorithm that minimizes mobile social networks' total weighted completion time. This deterministic algorithm achieves an approximation ratio of $\max\left{2.5,1+\epsilon\right}$ for $\epsilon>0$. Additionally, when the task's required service time or the total contact time between the requester and the crowd worker is sufficiently large, this algorithm can reach an approximation ratio of $1.5+\epsilon$ for $\epsilon>0$.