Modelling topological spatial relations: Strategies for query processing

Eliseo Clementini, Jayant Sharma, Max J. Egenhofer
1994 Computers & graphics  
This paper investigates the processing of spatial queries with topological constraints, for which current database solutions are inappropriate. Topological relations, such as disjoint, meet, overlap, inside, and contains, have been well defined by the 9-intersection, a comprehensive model for binary topological relations. We focus on two types of queries: (1) "Which objects have a stated topological relation with a given spatial object?" and (2) "What is the topological relation between two
more » ... n spatial objects?" Such queries are processed at two levels of detail. First, Minimum Bounding Rectangles are used as an approximation of the objects' geometry and as a means of identifying candidates that might satisfy the query. Next, the nine intesections that determine the topological relations between candidate pairs are calculated. We present algorithms for minimizing these computations. Considerable performance can be gained by exploiting the semantics of spatial relations. We also compare the approach for a naive cost model, which assumes that all relations have the same frequency of occurrence, with a refined cost model, which considers the probability of occurrence of the topological relations. The strategies presented here have three key benefits: (1) they are based on a well-defined formalism; (2) they are customizable; and (3) they can take into account important statistical information about the data. * This work was performed while on a leave the spatial data model and data structures used. An example of a heuristic would be the use of Minimum Bounding Rectangles (MBRs) as a first approximation of the objects' geometry as a fast filter. Estimates of the distribution are important, because the application often determines what relations are feasible. For example, in a cadastral application the only possible topological relations between land parcels are disjoint or meet. This paper focuses on the processing and algebraic optimization of spatial queries with topological constraints. An example of such a query is, "Find all residential lots for sale adjacent to Branch Lake," where adjacent is a topological relation. Such relations are usually not explicitly stored among spatial objects, but have to be inferred from the objects' geometry. For example, the fact that two land parcels are adjacent would be inferred from the fact that the two regions have a part of their boundaries, but no interior, in common. While existing DBMSs do not support such complex relations, extensible DBMSs [3] have the provisions to incorporate them into query languages. To be successful as geographic databases, extensible DBMSs need models of how to process and optimize queries over spatial relations.
doi:10.1016/0097-8493(94)90007-8 fatcat:muxxtvcaebdkvkmcqiozookgxi