In data stream applications, data arrive continuously and can only be scanned once as the query processor has very limited memory (relative to the size of the stream) to work with. Hence, queries on data streams do not have access to the entire data set and query answers are typically approximate. While there have been many studies on the k Nearest Neighbors (kNN) problem in conventional multidimensional databases, the solutions cannot be directly applied to data streams for the above reasons. In this paper, we investigate the kNN problem over data streams. We first introduce the e-approximate kNN (ekNN) problem that finds the approximate kNN answers of a query point Q such that the absolute error of the k-th nearest neighbor distance is bounded by e. To support ekNN queries over streams, we propose a technique called DISC (aDaptive Indexing on Streams by space-filling Curves). DISC can adapt to different data distributions to either (a) optimize memory utilization to answer ekNN ...