Maximising lifetime for fault-tolerant target coverage in sensor networks

We study the problem of maximising the lifetime of a sensor network for fault-tolerant target coverage in a setting with composite events. Here, a composite event is the simultaneous occurrence of a combination of atomic events, such as the detection of smoke and high temperature. We are given sensor nodes that have an initial battery level and can monitor certain event types, and a set of points at which composite events need to be detected. The points and sensor nodes are located in the Euclidean plane, and all nodes have the same sensing radius. The goal is to compute a longest activity schedule with the property that at any point in time, each event point is monitored by at least two active sensor nodes. We present a (6 + ε)-approximation algorithm for this problem by devising an approximation algorithm with the same ratio for the dual problem of minimising the weight of a fault-tolerant sensor cover and applying the Garg-Könemann algorithm. Our algorithm for the minimum-weight fault-tolerant sensor cover problem generalises previous approximation algorithms for geometric set cover with weighted unit disks and is obtained by enumerating properties of the optimal solution that guide a dynamic programming approach.