Optimizing lifetime of a wireless sensor network has received considerable attention in recent years. In this paper, using the feasibility and simplicity of grid-based clustering and routing schemes, we investigate optimizing lifetime of a two-dimensional wireless sensor network. Thus how to determine the optimal grid sizes in order to prolong network lifetime becomes an important problem. At first, we propose a model for lifetime of a grid in equal-grid model. We also consider that nodes can transfer packets to a grid which is two or more grids away in order to investigate the trade-off between traffic and transmission energy consumption. After developing the model for an adjustable-grid scenario, in order to optimize lifetime of the network, we derive the optimal values for dimensions of the grids. The results show that if radio ranges are adjusted appropriately, the network lifetime in adjustable-grid model is prolonged compared with the best case where an equal-grid model is used.

Sensor networks have promising applications such as battlefield surveillance, biological detection, and emergency navigation, etc. Crucial problems in sensor networks are energy-efficiency and collision avoidance in wireless communication. To deal with the problems, we consider a self-stabilizing solution to the construction of k disjoint sense-sleep trees, where range adjustment and the use of GPS are allowed. Each root is determined by its identifier and is distinguished by its color, the identification of a tree. Using a dominating k-partition rule, each non-root node first determines a color irrelevant to the root. Then, the non-root node determines a parent node that is equally colored with minimal distance. If there is no appropriate parent, the range is extended or shrunk until the nearest parent is determined. Finally, we perform a simulation.