Spatial aggregation: Data model and implementation

Data aggregation in Geographic Information Systems (GIS) is a desirable feature, only marginally present in commercial systems nowadays, mostly through ad hoc solutions. We address this problem introducing a formal model that integrates, in a natural way, geographic data and non-spatial information contained in a data warehouse external to the GIS. This approach allows both aggregation of geometric components and aggregation of measures associated to those components, defined in GIS fact tables. We define the notion of geometric aggregation, a general framework for aggregate queries in a GIS setting. Although general enough to express a wide range of (aggregate) queries, some of these queries can be hard to compute in a real-world GIS environment because they involve computing an integral over a certain area. Thus, we identify the class of summable queries, which can be efficiently evaluated replacing this integral with a sum of functions of geometric objects. Integration of GIS and OLAP (On Line Analytical Processing) is supported also through a language, GISOLAP-QL. We present an implementation, denoted Piet, which supports four kinds of queries: standard GIS, standard OLAP, geometric aggregation (like “total population in states with more than three airports”), and integrated GIS-OLAP queries (“total sales by product in cities crossed by a river”, also allowing navigation of the results). Further, Piet implements a novel query processing technique: first, a process called subpolygonization decomposes each thematic layer in a GIS, into open convex polygons; then, another process (the overlay precomputation) computes and stores in a database the overlay of those layers for later use by a query processor. Experimental evaluation showed that for a wide class of geometric queries, overlay precomputation outperforms R-tree-based techniques, suggesting that it can be an alternative for GIS query processing.