Decentralized querying of topological relations between regions monitored by a coordinate-free geosensor network

Geosensor networks present unique resource constraints to spatial computation, including limited battery power, communication constraints, and frequently a lack of coordinate positioning systems. As a result, there is a need for new algorithms that can efficiently satisfy basic spatial queries within those resource constraints. This paper explores the design and evaluation of a family of new algorithms for determining the topological relations between regions monitored by such a resource-constrained geosensor network. The algorithms are based on efficient, decentralized (in-network) variants of conventional 4-intersection and intersection and difference models, with in-network data aggregation. Further, our algorithms operate without any coordinate information, making them suitable applications where a positioning system is unavailable or unreliable. While all four algorithms are shown to have overall communication complexity O(n) and optimal load balance O(1), the algorithms differ in the level of topological detail they can detect; the types of regions they can monitor; and in the constant factors for communication complexity. The paper also demonstrates the impact of finite granularity observations on the correctness of the query results. In the conclusions, we identify the need to conduct further fundamental research on the relationship between topological relations between regions and limited granularity sensor observations of those regions.