Reverse Top-k Queries

Synonyms

R top-k queries

Definition

Given a query point q and a d-dimensional dataset S, a reverse top-k query returns the scoring functions for which q belongs to the top-k result set. The most important and commonly used case of scoring functions is the weighted sum function f_w() that is defined by a weighting vector w and computes the score of any data point p ∈ S, i.e., $f_w(p) =\sum _{i=1}^d w[i] \cdot p[i]$, where w[i] ≥ 0. For a point q and a positive number k, as well as two datasets S and W, where S represents data points and W is a dataset containing different weighting vectors, a weighting vector w_i ∈ W belongs to the reverse top-k result set of q, if and only if there exists a point p that belongs to the top-k result set of w_i such that $f_{w_i}(q) \leq f_{w_i}(p)$ (assuming that minimum values are preferable).

Main Text

Reverse top-k queries [1, 2] are useful in various real-life applications that exploit user preferences for data analysis tasks. For example,...