Efficiently implementable algebra for distributed in-network spatial analysis

Existing sensor network query processors (SNQPs) have demonstrated that in-network processing is an effective and efficient means of interacting with wireless sensor networks (WSNs) for data collection tasks. Inspired by these findings, this article investigates the question as to whether spatial analysis over WSNs can be built upon established distributed query processing techniques, but, here, emphasis is on the spatial aspects of sensed data, which are not adequately addressed in the existing SNQPs. By spatial analysis, we mean the ability to detect topological relationships between spatially referenced entities (e.g. whether mist intersects a vineyard or is disjoint from it) and to derive representations grounded on such relationships (e.g. the geometrical extent of that part of a vineyard that is covered by mist). To support the efficient representation, querying and manipulation of spatial data, we use an algebraic approach. We revisit a previously proposed centralized spatial algebra comprising a set of spatial data types and a comprehensive collection of operations. We have redefined and re-conceptualized the algebra for distributed evaluation and shown that it can be efficiently implemented for in-network execution. This article provides rigorous, formal definitions of the spatial data types, points, lines and regions, together with spatial-valued and topological operations over them. The article shows how the algebra can be used to characterize complex and expressive topological relationships between spatial entities and spatial phenomena that, due to their dynamic, evolving nature, cannot be represented a priori.