Decentralized querying of topological relations between regions without using localization

This paper proposes an efficient, decentralized algorithm for determining the topological relationship between two regions monitored by a geosensor network. Many centralized algorithms already exist for this purpose (used for example in spatial databases). However, these algorithms are not suited to decentralized spatial computing environments, like geosensor networks, which must operate without global knowledge of the system state and without centralized control. Unlike many existing decentralized spatial algorithms, the proposed algorithm is also able to operate in the absence of information about a node's coordinate location. This makes the algorithm suitable for applications of geosensor networks where GPS or other positioning systems are unavailable or unreliable. The algorithm approach is founded on the well-known 4-intersection model, using in-network data aggregation and spatial filtering (involving nodes only at some region boundaries). This ensures only a relatively small proportion of the network is involved in computation, thus increasing efficiency. Our analysis shows that while the overall communication complexity of the algorithm is O(n), the load balancing is optimal leading to a constant O(1) communication complexity for individual nodes. This expectation is confirmed with empirical investigation using simulation, which demonstrates the practical efficiency of the algorithm.