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Using a sliding window model, the top-<jats:italic>k<\/jats:italic> result changes as new sets enter the window or existing ones leave the window. Specifically, when a set arrives, it may form a new top-<jats:italic>k<\/jats:italic> result pair with any set already in the window. When a set leaves the window, all its pairings in the top-<jats:italic>k<\/jats:italic> result must be replaced with other pairs. It is therefore not sufficient to maintain the <jats:italic>k<\/jats:italic> most similar pairs since less similar pairs may become top-<jats:italic>k<\/jats:italic> pairs later. We propose SWOOP, a highly scalable stream join algorithm. Novel indexing techniques and sophisticated filters efficiently prune obsolete pairs as new sets enter the window. SWOOP incrementally maintains a provably minimal stock of similar pairs to update the top-<jats:italic>k<\/jats:italic> result at any time. 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