Algorithms for Wireless Communication and Sensor Networks

In this thesis we will address four problems concerned with algorithmic issues that arise from communication and sensor networks. The problem of scheduling wireless transmissions under SINR constraints has received much attention for unicast (one to one) transmissions. We consider the scheduling problem for multicast requests of one sender to many receivers, and present a logarithmic approximation algorithm and an online lower bound for arbitrary power assignments. We study the problem of maximising the lifetime of a sensor network for fault-tolerant target coverage in a setting with composite events, where a composite event is the simultaneous occurrence of one or more atomic events. We are the first to study this variation of the problem from a theoretical perspective, where each event must be covered twice and there are several event types, and we present a (6 + ɛ)-approximation algorithm for the problem. The online strongly connected dominating set problem concerns the construction of a dominating set that is strongly connected at all times, and for every vertex not in the dominating set, there exists an edge to some vertex in the dominating set, and an edge from a vertex in the dominating set. We present a lower bound for deterministic online algorithms and present an algorithm that achieves competitive ratio matching the lower bound. The monotone barrier resilience problem is to determine how many sensors must be removed from a sensor network, such that a monotone path can exist between two points that does not intersect any sensor. We present a polynomial time algorithm that can determine the monotone barrier resilience for sensor networks of convex pseudo-disks of equal width.