Abstract-Top-k query has long been an important topic in many fields of computer science. Efficient implementation of the top-k queries is the key for information searching. With the new frontier such as the 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, different users may request different set of information, with different priorities and at different times. Thus, the top-k search not only should be multi-dimensional, but also across time domain. From the system's perspective, the 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 resourceconstrained and system efficiency is of paramount importance.In this paper, we develop a framework that can effectively satisfy the two ends. The sensor network maintains an efficient dominant graph data structure for data readings. A simple topk extraction algorithm is used for the user query processing and two schemes are proposed to further reduce communication cost. Our proposed methods can be used for top-k query with any linear convex query function. To the best of our knowledge, this is the first work for continuous multi-dimensional top-k query processing in sensor networks; and our simulation results show that our schemes can reduce the total communication cost by up to 90%, compared with the centralized scheme or a straightforward extension from previous top-k algorithm on one-dimensional sensor data.