Approximating High-Dimensional Range Queries with kNN Indexing Techniques

While k-nearest neighbor queries are becoming increasingly common due to mobile and geospatial applications, orthogonal range queries in high-dimensional data are extremely important in scientific and web-based applications. For efficient querying, data is typically stored in an index optimized for either kNN or range queries. This can be problematic when data is optimized for kNN retrieval and a user needs a range query or vice versa. Here, we address the issue of using a kNN-based index for range queries, as well as outline the general computational geometry problem of adapting these systems to range queries. We refer to these methods as space-based decompositions and provide a straightforward heuristic for this problem. Using iDistance as our applied kNN indexing technique, we also develop an optimal (data-based) algorithm designed specifically for its indexing scheme. We compare this method to the suggested näıve approach using real world datasets and results show that our data-based algorithm consistently performs better.