Ranked Enumeration for Database Queries

Project page: Any-k

Shows that ranked and unranked enumeration of answers to database queries can be seen as two instances of the same algorithm.

Ranked enumeration is a query-answering paradigm where the query answers are returned incrementally in order of importance (instead of returning all answers at once). Importance is defined by a ranking function that can be specific to the application, but typically involves either a lexicographic order (e.g., "ORDER BY R.A, S.B" in SQL) or a weighted sum of attributes (e.g., "ORDER BY 3*R.A + 2*S.B"). We recently introduced any-k algorithms for (multi-way) join queries, which push ranking into joins and avoid materializing intermediate results until necessary. The top-ranked answers are returned asymptotically faster than the common join-then-rank approach of database systems, resulting in orders-of-magnitude speedup in practice.

In addition to their practical usefulness, our techniques complement a long line of theoretical research on unranked enumeration, where answers are also returned incrementally, but with no explicit ordering requirement. For a broad class of ranking functions with certain monotonicity properties, including lexicographic orders and sum-based rankings, the ordering requirement surprisingly does not increase the asymptotic time or space complexity, apart from logarithmic factors.

A key insight of our work is the connection between ranked enumeration for database queries and the fundamental task of computing the kth-shortest path in a graph. Uncovering these connections allowed us to ground our approach in the rich literature of that problem and connect ideas that had been explored in isolation before. In this article, we adopt a pragmatic approach and present a slightly simplified version of the algorithm without the shortest-path interpretation. We believe that this will benefit practitioners looking to implement and optimize any-k approaches.

In addition to their practical usefulness, our techniques complement a long line of theoretical research on unranked enumeration, where answers are also returned incrementally, but with no explicit ordering requirement. For a broad class of ranking functions with certain monotonicity properties, including lexicographic orders and sum-based rankings, the ordering requirement surprisingly does not increase the asymptotic time or space complexity, apart from logarithmic factors.

A key insight of our work is the connection between ranked enumeration for database queries and the fundamental task of computing the kth-shortest path in a graph. Uncovering these connections allowed us to ground our approach in the rich literature of that problem and connect ideas that had been explored in isolation before. In this article, we adopt a pragmatic approach and present a slightly simplified version of the algorithm without the shortest-path interpretation. We believe that this will benefit practitioners looking to implement and optimize any-k approaches.