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Top-k query has long been a crucial problem in multiple fields of computer science, such as data processing and information retrieval. In emerging cyber-physical systems, where there can be a large number of users searching information directly into the physical world, many new challenges arise for top-k query processing. From the client's perspective, users may request different sets of information, with different priorities and at different times. Thus, top-k search should not only be multidimensional, but also be across time domain. From the system's perspective, data collection is usually carried out by small sensing devices. Unlike the data centers used for searching in the cyber-space, these devices are often extremely resource constrained and system efficiency is of paramount importance. In this paper, we develop a framework that can effectively satisfy demands from the two aspects. The sensor network maintains an efficient dominant graph data structure for data readings. A simple top-k extraction algorithm is used for user query processing and two schemes are proposed to further reduce communication cost. Our methods can be used for top-k query with any linear convex query function. The framework is adaptive enough to incorporate some advanced features; for example, we show how approximate queries and data aging can be applied. To the best of our knowledge, this is the first work for continuous multidimensional top-k query processing in sensor networks. Simulation results show that our schemes can reduce the total communication cost by up to 90 percent, compared with a centralized scheme or a straightforward extension from previous top-k algorithm on 1D sensor data.