Master's Thesis Nr. 112
نویسندگان
چکیده
We present an indexing scheme that is capable of answering a broad range of complex top-k queries that contain a scalar product between two vectors when one of the vectors is present in the database, while the other one arrives at query time. Specifically we provide indexing facilities for the top-k closest points below (above) a hyperplane and the top-k farthest points below (above) a hyperplane, when the hyperplane is described by the scalar product equation 〈a,x〉 = b. The parameters a, b are parameters of the query, whereas the set of points that we query is materializable from the database. We provide in depth explanation of the algorithms and data structures that compose our indexing scheme. Furthermore, we evaluate and compare the performance of our index with an exhaustive search baseline algorithm, with different types of queries, on synthetic datasets. In addition to the baseline comparison, we compare our indexing scheme with an alternative solution method, that uses completely different approach. The space consumption of the index is parametrizable, and depending on the performance needs and available memory can range from extremely lightweight to more demanding. The query time complexity is logarithmic on the number of data points in the best case and linear on the number of data points in the worst case.
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