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The traditional relay deployment problem typically assumes that the locations of users are known and stationary, which is not realistic in practice. The prevalence of mobile devices has made it possible to collect user trajectory and account for user movement while deploying relays. Under this background, a novel problem trajectory-based relay deployment (TBRD) is put forward. This problem considers communication-related metrics and is aimed at maximizing user connection time as users roam through the target area under relay resource constraints, which is more reasonable than the goal of expanding the relay coverage. To figure out the TBRD, we first propose the concept demand nodes (DNs), which are virtual weighted nodes representing the locations where users frequently pass or stay for a long period. Next, we design a Demand Node Generation algorithm that can transform the continuous historical user trajectory into a number of discrete DNs. By generating DNs, we convert the TBRD problem into a demand node coverage (DNC) problem, which is proved to be NP-complete. Followed by that, we introduce an approximation algorithm, named Submodular Iterative Deployment Algorithm, which solves the DNC problem with the approximation factor $1-\frac{1}{\sqrt{e\cdot (1-1/k)}}$, where $e$ is the mathematical constant, and $k$ is the relay number constraint. Finally, five real trajectory datasets are used to evaluate our proposed algorithm, and the simulation results demonstrate that our algorithm can obtain high coverage for users in motion, which can lead to better user experience. In addition, we also analyze the impact of different parameters on the coverage performance, and under this circumstance, we may safely come to the conclusion that our work is at the leading edge to utilize user trajectories for relay deployment in wireless networks.

Crowdsourcing has become increasingly popular in recent years. In order to achieve the optimal task allocation, one of the most important issues is to select more suitable crowdworkers. By leveraging its pervasiveness, social network can be employed as a novel worker recruitment platform. A robust task allocation scheme over the social network could also consider the word-of-mouth (WoM) mode, in which tasks are delivered from workers to workers. In this paper, we discuss an Non-deterministic Polynomial-Hard (NP-Hard) problem, cost-effective and budget-balanced task allocation (CBTA) problem under the WoM mode in social groups. We propose two heuristic algorithms: CB-greedy and CB-local based on greedy strategy and local search technique, respectively. We also prove that the running time of CB-greedy is $O(m^2\log m)$, whereas CB-local utilizing disjoint-set achieves $O(mn\alpha (m, n))$, where $m$ is the number of edges indicating interactions of social groups, $n$ is the number of social groups and $\alpha $ is the inverse Ackerman function. Extensive experiments validate the efficiency and performance of our proposed algorithms.