Abstract. Existing work on multiway spatial joins focuses on the retrieval of all exact solutions with no time limit for query processing. Depending on the query and data properties, however, exhaustive processing of multiway spatial joins can be prohibitively expensive due to the exponential nature of the problem. Furthermore, if there do not exist any exact solutions, the result will be empty even though there may exist solutions that match the query very closely. These shortcomings motivate the current work, which aims at the retrieval of the best possible (exact or approximate) solutions within a time threshold, since fast retrieval of approximate matches is the only way to deal with the ever increasing amounts of multimedia information in several real time systems. We propose various techniques that combine local and evolutionary search with underlying indexes to prune the search space. In addition to their usefulness as standalone methods for approximate query processing, the techniques can be combined with systematic search to enhance performance when the goal is retrieval of the best solutions.

The user of a Geographical Information System is not limited to conventional spatial selections and joins, but may also pose more complicated and descriptive queries. In this paper, we focus on the ef®cient processing and optimization of complex spatial queries that involve combinations of spatial selections and joins. Our contribution is manifold; we ®rst provide formulae that accurately estimate the selectivity of such queries. These formulae, paired with cost models for selections and joins can be used to combine spatial operators in an optimal way. Second, we propose algorithms that process spatial joins and selections simultaneously and are typically more ef®cient than combinations of simple operators. Finally we study the problem of optimizing complex spatial queries using these operators, by providing (i) cost models, and (ii) rules that reduce the optimization space signi®cantly. The accuracy of the selectivity models and the ef®ciency of the proposed algorithms are evaluated through experimentation.

Abstract. This papers deals with multiway spatial joins when (i) there is limited time for query processing and the goal is to retrieve the best possible solutions within this limit (ii) there is unlimited time and the goal is to retrieve a single exact solution, if such a solution exists, or the best approximate one otherwise. The first case is motivated by the high cost of join processing in real-time systems involving large amounts of multimedia data, while the second one is motivated by applications that require "negative" examples. We propose several search algorithms for query processing under theses conditions. For the limited-time case we develop some non-deterministic search heuristics that can quickly retrieve good solutions. However, these heuristics are not guaranteed to find the best solutions, even without a time limit. Therefore, for the unlimited-time case we describe systematic search algorithms tailored specifically for the efficient retrieval of a single solution. Both types of algorithms are integrated with R-trees in order to prune the search space. Our proposal is evaluated with extensive experimental comparison.