Identifying Surrounds and Engulfs Relations in Mobile and Coordinate-Free Geosensor Networks

Abstract

This article concerns the definition and identification of qualitative spatial relationships for the full and partial enclosure of spatial regions. The article precisely defines three relationships between regions—“surrounds,” “engulfs,” and “envelops”—highlighting the correspondence to similar definitions in the literature. An efficient algorithm capable of identifying these qualitative spatial relations in a network of dynamic (mobile) geosensor nodes is developed and tested. The algorithms are wholly decentralized, and operate in-network with no centralized control. The algorithms are also “coordinate-free,” able to operate in distributed spatial computing environments where coordinate locations are expensive to capture or otherwise unavailable. Experimental evaluation of the algorithms designed demonstrates the efficiency of the approach. Although the algorithm communication complexity is dominated by an overall worst-case O ( n 2 ) leader election algorithm, the experiments show in practice an average-case complexity approaching linear, O ( n 1.1 ).