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Wireless Sensor Networks (WSNs) are networks consisting of many small sensor nodes capable of wireless communication, and they are used for environmental monitoring, border guards, and so on. Among many types of WSNs, data gathering WSN periodically collects to a sink node environmental information such as temperature and amount of sunlight at each point in a wide agricultural area or forest. Some data gathering WSN applications need sufficient sensing quality and robustness of the system, and such systems may require k-coverage1 of the target sensing field. Data gathering WSNs that require k-coverage of the field should also operate for a long term. Thus, many research efforts have been devoted to the k-coverage problem and the WSN lifetime extension problem. In order to make such aWSN operate for a long term, Tang et al. reduced power consumption by regulating communication frequency among sensor nodes [Tang et al. (2006)]. Heinzelman et al. reduced total data transmission bymerging the data received frommultiple sensor nodes [Heinzelman et al. (2000)]. However, since the above existing approaches degrade sensing quality with respect to collected data amount and sensing frequency, some applications that always need sufficient sensing quality may not accept such a quality degradation. Cao, et al. proposed a sleep scheduling method which lets nodes sleep when they need not communicate, in order to save the overall power consumption in WSN [Cao et al. (2005)]. Keshavarzian, et al. proposed amethod tominimize active nodes and guarantee that the event information sensed by sensor nodes arrives to the sink node in a specified time [Keshavarzian et al. (2006)]. In thesemethods, sleeping nodes consume small power, but do not communicate with other nodes, and become active after specified time interval. These existing methods target applications collecting events occurring rarely and do not consider the field k-coverage. In order to k-cover the field, Poduri et al. used mobile sensor nodes to k-cover the target sensing field in short time under the constraint that for each sensor node, k other sensor nodes always exist in its proximity [Poduri et al. (2004)]. They also discussed about the optimal locations of sensor nodes for k-covering the field. This method does not consider maintaining k-coverage of the field for a long time though it makes k-coverage in short time.

Maximizing Lifetime of Data Gathering Wireless Sensor Network