Top-K Queries

We consider the recently introduced monochromatic reverse top-k queries which ask for, given a new tuple q and a dataset D, all possible top-k queries on D union {q} for which q is in the result. Towards this problem, we focus on designing indexes in two dimensions for repeated (or batch) querying, a novel but practical consideration. We present the insight that by representing the dataset as an arrangement of lines, a critical k-polygon can be identified and used exclusively to respond to reverse top-k queries. We construct an index based on this observation which has guaranteed worst-case query cost that is logarithmic in the size of the k-polygon.

Abstract: Regret minimizing sets are a very recent approach to representing a dataset D with a small subset S of representative tuples. The set S is chosen such that executing any top-1 query on S rather than D is minimally perceptible to any user. To discover an optimal regret minimizing set of a predetermined cardinality is conjectured to be a hard problem. In this paper, we generalize the problem to that of finding an optimal k $ regret minimizing set, wherein the difference is computed over top-k queries, rather than top-1 queries.

The way that we interact with databases has changed. The ubiquitous textbook example of finding employees with salaries over 60K and ages under 30 no longer reflects a typical use case in modern applications; instead, users are interested in books, movies, music, documents, services, and users that are similar to another object that they have in mind. This sort of similarity search is often implemented by means of a top-k query, wherein each tuple is assigned a score and the tuples with the k highest scores are reported back to the user.