Algorithms for Answering Geo-Range Query

In wireless sensor networks, we usually need to detect interesting events based on the information gathered from multiple sensors. One useful detection is to test whether or not the average sensory value within an area is larger than a given threshold. Such type of query is called geo-range query. It should report the geographic centers where the average value of nearby sensors is greater than a certain threshold. Answering geo-range query is nontrivial because we do not know in advance the satisfying geographic centers, which may not be necessarily the same as the locations of sensors. We develop two efficient algorithms: the brute-force search algorithm and the sweep-line algorithm. The brute-force search algorithm uses exhaustive search to enumerate all possible satisfying sub-regions. Its time complexity is O(n³), where n is the number of sensor nodes. The sweep-line algorithm uses a virtual line sweeping top-down through the plane. The algorithm takes O(n² log n) running time, and still obtains exact solution to the problem.