A key challenge in developing energy-efficient sensor networks is to extend network lifetime in resource-limited environments. As sensors are often densely distributed, they can be scheduled on alternative duty cycles to conserve energy while satisfying the system requirements. Directional sensor networks composed of a large number of directional sensors equipped with a limited battery and with a limited angle of sensing have recently attracted attention. Many types of directional sensors can rotate to face a given direction. Maximizing network lifetime while covering all of the targets in a given area and forwarding sensor data to the sink is a challenge in developing such rotatable directional sensor networks. In this paper, we address the maximum directional cover tree (MDCT) problem of organizing directional sensors into a group of non-disjoint subsets to extend network lifetime. One subset, in which the directional sensors cover all of the targets and forward the data to the sink, is activated at a time, while the others sleep to conserve energy. For the MDCT problem, we first present an energy-consumption model that mainly takes into account the energy expenditure for sensor rotation as well as for the sensing and relaying of data. We also develop a heuristic scheduling algorithm called directional coverage and connectivity (DCC)-greedy to solve the MDCT problem. To verify and evaluate the algorithm, we conduct extensive simulations and show that it extends network lifetime to a reasonable degree.

In this paper, a novel algorithm, Cross Low-dimension Pursuit, based on a new structured sparse matrix, Permuted Block Diagonal (PBD) matrix, is proposed in order to recover sparse signals from incomplete linear measurements. The main idea of the proposed method is using the PBD matrix to convert a high-dimension sparse recovery problem into two (or more) groups of highly low-dimension problems and crossly recover the entries of the original signal from them in an iterative way. By sampling a sufficiently sparse signal with a PBD matrix, the proposed algorithm can recover it efficiently. It has the following advantages over conventional algorithms: (1) low complexity, i.e., the algorithm has linear complexity, which is much lower than that of existing algorithms including greedy algorithms such as Orthogonal Matching Pursuit and (2) high recovery ability, i.e., the proposed algorithm can recover much less sparse signals than even 1-norm minimization algorithms. Moreover, we demonstrate both theoretically and empirically that the proposed algorithm can reliably recover a sparse signal from highly incomplete measurements.