Verification of k-coverage on query line segments

The coverage problem is one of the fundamental problems in sensor networks, which reflects the degree of a region being monitored by sensors. In this paper, we make the first attempt to address the k-coverage verification problem regarding a given query line segment, which returns all sub-segments from the line segment that are covered by at least k sensors. To deal with the problem, we propose three methods based on the R-tree index. The first method is the most primitive one, which identifies all intersection points of the query line segment and the circumferences of the covering regions of the sensors and then checks each sub-segment to see whether it is k-coverage. Improving from the first method, the second method calculates the lower bound of the number of sensors covering a specific sub-segment to reduce the computation costs. The third method partitions the query line segment into sub-segments with equal length and then verifies each of them. A series of experiments on a real dataset and two synthetic datasets are performed to evaluate these methods. The experiment results demonstrate that the third method has the best performance among all three methods.