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Moving objects databases managing spatial objects with continuously changing position and extent over time have recently found large interest in the database community. Queries about moving objects become particularly interesting when they ask for temporal changes in the topological relationships between evolving spatial objects. A concept of spatio-temporal predicates has been proposed to describe these relationships. The goal of this paper is to design efficient algorithms for them so that they can be used in spatio-temporal joins and selections. This paper proposes not to design an algorithm for each new predicate individually but to employ a generic algorithmic scheme, which is able to cover present and future predicate definitions.