Energy Efficient Monitoring in Sensor Networks
Lecture Notes in Computer Science
In this paper we study a set of problems related to efficient energy management for monitoring applications in wireless sensor networks. We study several generalizations of a basic problem called Set k-Cover. The problem can be described as follows: we are given a set of sensors, and a set of regions to be monitored. Each region can be monitored by a subset of the sensors. To increase the lifetime of the sensor network, we would like to partition the sensors into k sets (or time-slots), and
... ime-slots), and activate each set of sensors in a different time-slot, thus extending the battery life of the sensors by a factor of k. The goal is to find a partitioning that maximizes the total coverage of the regions for a given k. This problem is known to be N P -hard. We develop an improved approximation algorithm for this problem using a reduction to Max k-Cut. Moreover, we are able to demonstrate that this algorithm is practical, and yields almost optimal solutions in practice. We also consider generalizations of this problem in several different directions. First, we allow each sensor to be active in α different sets (time-slots). This means that the battery life is extended by a factor of k α , and allows for a richer space of solutions. We also consider different coverage requirements, such as requiring that all regions, or at least a certain number of regions, be covered in each time slot. In the Set k-Cover formulation, there is no requirement that a region be monitored at all, or in any number of time slots. We develop a randomized rounding algorithm for this problem. We also consider extensions where each sensor can monitor only a bounded number of regions in any time-slot, and not all the regions adjacent to it. This kind of problem may arise when a sensor has a directional camera, or some other physical constraint might prevent it from monitoring all adjacent regions even when it is active. We develop the first approximation algorithms for this problem.