Compact Representation of Spatial Hierarchies and Topological Relationships

The topological model for spatial objects identifies common boundaries between regions, explicitly storing adjacency relations, which not only improves the efficiency of topologyrelated queries, but also provides advantages such as avoiding data duplication and facilitating data consistency. Recently, a compact representation of the topological model based on planar graph embeddings was proposed. In this article, we provide an elegant generalization of such a representation to support hierarchies of vector objects, which better fits the multi-granular nature of spatial data, such as the political and administrative partition of a country. This representation adds a small space on top of the succinct base representation of each granularity, while efficiently answering new topology-related queries between objects not necessarily at the same level of granularity.