Simple geometric constructs for routing and boundary detection in sensor networks

Micro-sensor and radio technologies now permit the manufacture of cheap sensor or embedded devices deployable en masse. Applications appear in a diverse set of environments for far reaching applications including but not limited to structural monitoring, target tracking, and early warning systems. When deployed to create a sensor network, have no foreknowledge of their environment. In a network of this type traditional networking techniques are unsuitable. In general, sensing and embedded devices are shaped by four constraints: limited power supply, small memory, unattended operation, and the error-prone nature of wireless communications.;Our work is motivated by the hypothesis that within view of each node are geometric features that impact network characteristics and behaviour. The central objective in this thesis is to investigate the geometry of the network graphs. Doing so allows us to identify some of the unique features of the network that constrain larger problems.;We first propose boundary detection solutions using two well-known structures. First with the convex hull we build a localised heuristic, local convex view (lcv), that is designed on the premise that a node on the convex hull of a small region of the network is likely on the convex hull of the whole network. We show positive results via analysis and simulation and discover that the geometric properties are directly responsible for its resilience to error. We propose further the alpha-hull. whose structure can reveal details in the 'shape' of a set of points. We find that by selecting the alpha-parameter carefully, it is possible to infer the network-wide alpha-hull from local communications and computations.;We also investigate the limits of routing according to left- or right-hand rule (LHR). Using LHR, a node upon receipt of a message will forward to the neighbour that sits next in counter-clockwise order in the network graph. When used to recover from greedy routing failures, LHR guarantees success if implemented over planar graphs. We identify network constraints that lead us to propose the Prohibitive-link Detection and Routing Protocol (PDRP) that can guarantee delivery over non-planar graphs. As the name implies, the protocol detects and circumvents 'bad' links. Our implementation of PDRP reveals the same level of service as face-routing protocols despite preserving most intersecting links in the network.