The widespread use of social-media graphs has provided a convenient channel for rumor propagation. Rapid localization of rumor sources is therefore crucial for mitigating diffusion and enabling punitive countermeasures. Source Localization (SL) aims to identify the origin nodes given partial infection observations. Although deep-learning-based SL approaches outperform traditional estimators, three fundamental limitations remain: (i) Model Complexity —existing methods enrich node embeddings with cascades of auxiliary features, yielding high-capacity but excessively complex representations, leading to an exponential increase in the number of model parameters; (ii) Annotation gap —to overcome the scarcity of real-world misinformation cascades, current pipelines repeatedly simulate diffusion from a fixed seed, eroding robustness on true, few-shot outbreaks; and (iii) Computational bottleneck —full-model retraining or recurrent cascade simulation is required for every new task, which disqualifies the solutions from real-time deployment. Inspired by the success of prompt learning in NLP and graph learning, we propose LAPS, a Lightweight privilege-Allocation Prompting framework for Source localization. LAPS first trims parameter explosion and data scarcity by pre-training a graph-level source region classifier on adaptive subgraphs with source-prior diffusion data. It then enables few-shot SL via a privilege-allocation prompt module that updates <1% of all the parameters, avoiding model retraining to facilitate efficiency. Extensive experiments on five real-world networks demonstrate the effectiveness and efficiency of our prompt-based framework on few-shot source localization task.

Vehicular crowdsensing employs vehicles as mobile sensing nodes to collect road environmental information and process the collected data. To perform the delay-tolerant crowdsensing tasks in convenience, vehicles with computational demands can offload the data process tasks to a proximal edge server (ES) in a probabilistic manner after entering a parking lot. The ES determines how to price the offloading services to maximize the expected total revenue, causing a joint probabilistic data offloading and service pricing problem between the vehicles and ES. To address the problem, we adopt a Stackelberg game approach to study the interaction between them. Specifically, the ES plays as the leader to determine the uniform price for all offloading vehicles, and to equally allocate the computing resource among them. The vehicles play as the followers to optimize their offloading probabilities to minimize the expected weighted sum of task delay, energy consumption and service fee. We employ the backward induction method to analyze the unique Stackelberg equilibrium. Subsequently, a distributed algorithm is designed to reach the Stackelberg equilibrium without prior knowledge of the vehicles. Numerical results demonstrate that compared with the baseline schemes, our scheme has an advantage in improving the economic benefits of the ES.