Full-view area coverage in camera sensor networks: Dimension reduction and near-optimal solutions

We study the problem of minimum-number full-view area coverage in camera sensor networks, i.e., how to select the minimum number of camera sensors to guarantee the full-view coverage of a given region. Full-view area coverage is challenging because the full-view coverage of a 2-D continuous domain has to be considered. To tackle this challenge, we first study the intrinsic geometric relationship between the full-view area coverage and the full-view point coverage and prove that the full-view area coverage can be guaranteed, as long as a selected full-view ensuring set of points is full-view covered. This leads to a significant dimension reduction for the full-view area coverage problem. Next, we prove that the minimum-number full-view point coverage is NP-hard and propose two approximation algorithms to solve it from two different perspectives, respectively: 1) By introducing a full-view coverage ratio function, we quantify the "contribution" of each camera sensor to the full-view coverage through which we transform the full-view point coverage into a submodular set cover problem and propose a greedy algorithm (GA); and 2) by studying the geometric relationship between the full-view coverage and the traditional coverage, we propose a set-cover-based algorithm (SCA). We analyze the performance of these two approximation algorithms and characterize their approximation ratios. Furthermore, we devise two distributed algorithms that obtain the same approximation ratios as GA and SCA, respectively. Finally, we provide extensive simulation results to validate our analysis.