Uncertainty is inherent in many important applications, such as location-based services (LBS), sensor monitoring and radio-frequency identification (RFID). Recently, considerable research efforts have been put into the field of uncertainty-aware spatial query process-ing. In this paper, we study the problem of finding top k most influ-ential facilities over a set of uncertain objects, which is an impor-tant spatial query in the above applications. Based on the maximal utility principle, we propose a new ranking model to identify the top k most influential facilities, which carefully captures influence of facilities on the uncertain objects. By utilizing two uncertain object indexing techniques, R-tree and U-Quadtree, effective and efficient...