With the proliferation of smartphones, participatory sensing using smartphones provides unprecedented opportunities for collecting enormous sensing data. There are two crucial requirements in participatory sensing, fair task allocation and energy efficiency, which are particularly challenging given high combinatorial complexity, tradeoff between energy efficiency and fairness, and dynamic and unpredictable task arrivals. In this paper, we present a novel fair energy-efficient allocation framework whose objective is characterized by min-max aggregate sensing time. We rigorously prove that optimizing the min-max aggregate sensing time is NP hard even when the tasks are assumed as a priori. We consider two allocation models: offline allocation and online allocation. For the offline allocation model, we design an efficient approximation algorithm with the approximation ratio of 2 - 1/m, where m is the number of member smartphones in the system. For the online allocation model, we propose a greedy online algorithm which achieves a competitive ratio of at most m. The results demonstrate that the approximation algorithm reduces over 81% total sensing time, the greedy online algorithm reduces more than 73% total sensing time, and both algorithms achieve over 3x better min-max fairness.

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