Spatial Database Management Systems (SDBMS), e.g., Geographical
Information Systems, that manage spatial objects such as points, lines, and hyper-rectangles, often have very high query processing costs. Accurate selectivity estimation during query optimization therefore is crucially important for finding good query plans, especially when spatial joins are involved. Selectivity estimation has been studied for relational database systems, but to date has only received little attention in SDBMS. In this paper, we introduce novel methods that permit high-quality selectivity estimation for spatial joins and range queries. Our techniques can be constructed in a single scan over the input, handle inserts and deletes to the database incrementally, and hence they can also be used for processing of streaming spatial data. In contrast to previous approaches, our techniques return approximate results that come with provable probabilistic quality guarantees. We present a detailed analysis and experimentally demonstrate the efficacy of the proposed techniques.