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Dispersed computing is a new resource-centric computing paradigm, which makes use of idle resources in the network to complete the tasks. Effectively allocating tasks between task nodes and networked computation points (NCPs) is a critical factor for maximizing the performance of dispersed computing. Due to the heterogeneity of nodes and the priority requirements of tasks, it brings great challenges to the task allocation in dispersed computing. In this paper, we propose a task allocation model based on incomplete preference list. The requirements and permissions of task nodes and NCPs are quantitatively measured through the preference list. In the model, the task completion rate, response time, and communication distance are taken as three optimizing parameters. To solve this NP-hard optimization problem, we develop a new many-to-many matching algorithm based on incomplete preference list. The unilateral optimal and stable solution of the model are obtained. Taking into account the needs for location privacy-preserving, we use the planar Laplace mechanism to produce obfuscated locations instead of real locations. The mechanism satisfies ε-differential privacy. Finally, the efficacy of the proposed model is demonstrated through extensive numerical analysis. Particularly, when the number of task nodes and NCPs reaches 1:2, the task completion rate can reach 99.33%.