Geometric approaches for creating low power, low interference connectivity patterns in static, structureless sensor networks

The technological as well as software advances in microelectronics and embedded component design have led to the development of low cost, small-sized devices capable of forming wireless, ad-hoc networks and sensing a number of qualities of their environment, while performing computations that depend on the sensed qualities as well as information received by their peers. These sensor networks rely on the collective power of the separate devices as well as their computational and sensing capabilities to understand “global” environmental states through locally sampled information and local sensor interactions. Due to the locality of the sensor networks, that naturally arises due to the locality of their communications capabilities, a number of interesting connections exist between these networks and geometrical concepts and problems. In this paper we study two simple problems that pertain to the formation of low power and low interference communication patterns in fixed topology sensor networks. We study the problem of using multihop communication links instead of direct ones as well as the problem of forming a communication ring of sensor networks so as to reduce power consumption as well as interference from other nodes. Our focus is on the connection between sensor networks and geometrical concepts, rather than on practicality, so as to highlight their interrelationship.