Optimal Algorithms for Ranked Enumeration of Answers to Full Conjunctive Queries
Generalizes dynamic programming over certain algebraic structures called "selective dioids" to optimal ranked enumeration of answers. Applies the theory to the special case of ranked enumeration over conjunctive queries. We call it "any-k" to emphasize the marriage of "anytime algorithms" with top-k.
We study ranked enumeration of the results to a join query in order of decreasing importance, as imposed by an appropriate ranking function. Our main contribution is a framework for ranked enumeration over a class of Dynamic Programming problems that generalizes seemingly different problems that to date had been studied in isolation. To this end, we study and extend classic algorithms that find the k-shortest paths in a weighted graph. For full conjunctive queries, including cyclic ones, our approach is asymptotically optimal in terms of (1) time to return the top result, (2) delay between results, and (3) time until all results are returned in order. These optimality properties were derived for a complexity measure that has been widely used in the context of worst-case optimal join algorithms, but which abstracts away factors that only depend on query size and a polylogarithmic cost factor in input size. By performing a more detailed cost analysis, we are able to uncover a previously unknown tradeoff between two incomparable enumeration approaches: one has lower complexity when the number of returned results is small, the other when it is large. We demonstrate theoretically and empirically the superiority of our techniques to batch algorithms that produce the full result and then sort it. Interestingly, our technique is not only faster for returning the first few results, but even when all results are produced.