ÐSelection and join queries are fundamental operations in Data Base Management Systems (DBMS). Support for nontraditional data, including spatial objects, in an efficient manner is of ongoing interest in database research. Toward this goal, access methods and cost models for spatial queries are necessary tools for spatial query processing and optimization. In this paper, we present analytical models that estimate the cost (in terms of node and disk accesses) of selection and join queries using R-treebased structures. The proposed formulae need no knowledge of the underlying R-tree structure(s) and are applicable to uniform-like and nonuniform data distributions. In addition, experimental results are presented which show the accuracy of the analytical estimations when compared to actual runs on both synthetic and real data sets.

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Without geospatial data management, today’s challenges in big data applications such as earth observation, geographic information system/building information modeling (GIS/BIM) integration, and 3D/4D city planning cannot be solved. Furthermore, geospatial data management plays a connecting role between data acquisition, data modelling, data visualization, and data analysis. It enables the continuous availability of geospatial data and the replicability of geospatial data analysis. In the first part of this article, five milestones of geospatial data management research are presented that were achieved during the last decade. The first one reflects advancements in BIM/GIS integration at data, process, and application levels. The second milestone presents theoretical progress by introducing topology as a key concept of geospatial data management. In the third milestone, 3D/4D geospatial data management is described as a key concept for city modelling, including subsurface models. Progress in modelling and visualization of massive geospatial features on web platforms is the fourth milestone which includes discrete global grid systems as an alternative geospatial reference framework. The intensive use of geosensor data sources is the fifth milestone which opens the way to parallel data storage platforms supporting data analysis on geosensors. In the second part of this article, five future directions of geospatial data management research are presented that have the potential to become key research fields of geospatial data management in the next decade. Geo-data science will have the task to extract knowledge from unstructured and structured geospatial data and to bridge the gap between modern information technology concepts and the geo-related sciences. Topology is presented as a powerful and general concept to analyze GIS and BIM data structures and spatial relations that will be of great importance in emerging applications such as smart cities and digital twins. Data-streaming libraries and “in-situ” geo-computing on objects executed directly on the sensors will revolutionize geo-information science and bridge geo-computing with geospatial data management. Advanced geospatial data visualization on web platforms will enable the representation of dynamically changing geospatial features or moving objects’ trajectories. Finally, geospatial data management will support big geospatial data analysis, and graph databases are expected to experience a revival on top of parallel and distributed data stores supporting big geospatial data analysis.

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It has been recently recognized that fuzzy set theory provides useful concepts and tools for both the representation and analysis of the uncertainty related to geographical data. Hence the incorporation of fuzzy set methodologies into a DBMS repository for the application domain of GIS should be bene® cial and will improve its level of intelligence. Focusing in this area the paper addresses both a representation and a reasoning issue. Speci® cally, it extends a general spatial data model to deal with the uncertainty of geographical entities, and shows how the standard data interpretation operations available in GIS packages may be extended to support the fuzzy spatial reasoning. Representative geographical operations, such as the fuzzy overlay, fuzzy distance and fuzzy select, are examined, while several real world examples are given.