Optimal algorithms for evaluating rank joins in database systems

Abstract

In the rank join problem, we are given a set of relations and a scoring function, and the goal is to return the join results with the top K scores. It is often the case in practice that the inputs may be accessed in ranked order and the scoring function is monotonic. These conditions allow for efficient algorithms that solve the rank join problem without reading all of the input. In this article, we present a thorough analysis of such rank join algorithms. A strong point of our analysis is that it is based on a more general problem statement than previous work, making it more relevant to the execution model that is employed by database systems. One of our results indicates that the well-known HRJN algorithm has shortcomings, because it does not stop reading its input as soon as possible. We find that it is NP-hard to overcome this weakness in the general case, but cases of limited query complexity are tractable. We prove the latter with an algorithm that infers provably tight bounds on the potential benefit of reading more input in order to stop as soon as possible. As a result, the algorithm achieves a cost that is within a constant factor of optimal.

Top-k Linked Data Query Processing

“…-We show that in a Linked Data setting, more detailed score information is available. We propose strategies for using this knowledge to provide tighter score bounds (and thus allow an earlier termination) as compared to top-k processing in other scenarios [2,13,17]. Further, we propose an aggressive technique for pruning partial query results that cannot contribute to the final top-k result.…”

“…Top-k query processing [14,7,17] aims at a more efficient query execution by focusing on the k best results, while skipping the computation of remaining results. This early termination can lead to a significant reduction in the number of inputs to be read and processed, which translates to performance improvements.…”

“…Besides the source index employed for Linked Data query processing, we need a ranking function as well as a sorted access for top-k processing [7,14,17].…”

“…However, previous work on the top-k join problem uses pull-based processing, i.e., join operators actively "pull" their inputs in order to produce an output [7,17,20]. In compliance with [17], we adapt the pull/bound rank join (PBRJ) algorithm template for a push-based execution in the Linked Data setting. For simplicity, the following presentation of the PBRJ algorithm assumes binary joins (i.e., each join has two inputs).…”

“…As reported in [17], the PBRJ has two parameters: its bounding strategy B and its pulling strategy P. For the former, the corner-bound is commonly employed and is also used in our approach. The latter strategy, however, is proposed for a pull-based execution and is thus not directly applicable.…”