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The paper is concerned with the effective and efficient processing of spatiotemporal selection queries under varying degrees of approximation. Such queries may employ operators like overlaps, north, during, etc., and their result is a set of entities standing approximately in some spatiotemporal relation with respect to a query object X. The contribution of our work is twofold: i) First we describe a mathematical framework for representing multidimensional relations at varying granularity levels, modelling relation approximation through the concept of relation convexity. ii) We subsequently exploit the framework for developing approximate spatiotemporal retrieval mechanisms, employing a set of existing as well as new main memory and secondary memory data structures that achieve either optimal or the best known performance in terms of time and space complexity, for both static and dynamic problems. 2VERVIEW The handling of spatiotemporal information is an increasingly evident demand for modern DBMSs, initially motivated by applications like GIS, CAD, etc. and soon expanded in areas such as robotics, medical imaging, multimedia applications, etc. (GG98). Efficient query processing for this type of data is a feature of primary importance. Spatiotemporal databases are collections of entities which have either spatial attributes (e.g. geographic databases) or temporal attributes (e.g. medical databases) or combinations thereof (e.g. multimedia databases). Spatial attributes can be viewed as 0D, 1D, 2D or 3D positions in a "space", either the physical one (e.g. map objects) or an artificial one such as a computer screen (e.g. multimedia objects). Temporal attributes capture the temporal existence of entities and in the general case can be represented as time points or time intervals. In order to support querying of such attributes, a DBMS must provide appropriate operators, usually in the form of binary spatial and temporal predicates (or relations), such as contains, west, near, after, etc. (e.g. "find all buldings northeast of the park built during 1970-1980"). A main category of queries of this sort is the class of spatiotemporal selection queries which ask for all entities standing in some spatiotemporal relation to a query object X. The processing of such selection queries gives rise to three main requirements, which are addressed in this work: a formal framework for the effective representation of spatiotemporal relations handling of approximate matches appropriate data structures for efficient query processing The study of binary spatial and temporal relations have been traditionally among the research interests of the DB and AI communities, respectively (see (PS94, Ege97, Kau, All83)). This interaction has yielded an abundance of models, which however suffer from a particular limitation: they allow for the representation of fixed sets of relations, thus restricting the potential range of applications. To our knowledge, no existing model provides varying granularity levels in the description of relations. Moreover, there is no universally accepted uniform spatiotemporal model. Responding to these requirements, we propose a multidimensional relation framework that can be tuned in various relation detail levels, which is based on 1D partitions called resolution schemes. The set of feasible relations at every resolution level are represented as binary strings which are characterised by an inherent poset structure, called conceptual neighbourhood, which provides certain desirable properties. An early informal description of the relation framework has been presented in (PMD98) and applied for 2D configuration retrieval (queries that ask for a set of objects that satisfy a particular spatial configuration), whereas a rigorous formulation can be found in (DH99). Section 2 in this paper borrows from the latter the concepts that pertain to spatiotemporal selection queries and provides the corresponding relation background. Unlike traditional selection queries where the output consists of a set of exact matches, in spatiotemporal queries we are equally interested in approximate matches as well, because i) inherently, answers closely similar to an exact match are not equally important to dissimilar ones, and ii) there are no universally accepted semantics for some spatiotemporal predicates like north-

A provably efficient computational model for approximate spatiotemporal retrieval