Determining the impact regions of competing options in preference space

In rank-aware processing, user preferences are typically represented by a numeric weight per data attribute, collectively forming a weight vector. The score of an option (data record) is defined as the weighted sum of its individual attributes. The highest-scoring options across a set of alternatives (dataset) are shortlisted for the user as the recommended ones. In that setting, the user input is a vector (equivalently, a point) in a d-dimensional preference space, where d is the number of data attributes. In this paper we study the problem of determining in which regions of the preference space the weight vector should lie so that a given option (focal record) is among the top-k score-wise. In effect, these regions capture all possible user profiles for which the focal record is highly preferable, and are therefore essential in market impact analysis, potential customer identification, profile-based marketing, targeted advertising, etc. We refer to our problem as k-Shortlist Preference Region identification (kSPR), and exploit its computational geometric nature to develop a framework for its efficient (and exact) processing. Using real and synthetic benchmarks, we show that our most optimized algorithm outperforms by three orders of magnitude a competitor we constructed from previous work on a different problem.