Monitoring Schedules for Randomly Deployed Sensor Networks Without Geographic Information

Given n sensors and m targets, a monitoring schedule is a partition of the sensor set such that each part of the partition can monitor all targets. Monitoring schedules are used to maximize the time all targets are monitored when there is no possibility of replacing the batteries of the sensors. Each part of the partition is used for one unit of time, and thus the goal is to maximize the number of parts in the partition. We present distributed algorithms for Monitoring Schedule under the following assumptions: 1) identical sensors can each monitor all targets within a certain radius, 2) the n sensors are randomly distributed uniformly in a large square containing the targets, 3) the number of sensors is high enough given the area the square, and 4) the communication range is at least a constant times the sensing range. We present randomized distributed algorithms that achieve a constant factor approximation in polylogarithmic number of communication rounds, with high probability. These results hold if we make one of the following two assumptions: 1) any two sensors within communication range are able to estimate within a constant their relative distance, or 2) the communication range is an exact fraction of the sensing range. We improve the results of Calinescu and Ellis (DIAL M-POMC ´08) by eliminating the assumption that the communication range must be twice the sensing range, and by this result holding with fewer sensors.