Regret-minimizing representative databases

Abstract

We propose the k -representative regret minimization query ( k -regret) as an operation to support multi-criteria decision making. Like top- k , the k -regret query assumes that users have some utility or scoring functions; however, it never asks the users to provide such functions. Like skyline, it filters out a set of interesting points from a potentially large database based on the users' criteria; however, it never overwhelms the users by outputting too many tuples. In particular, for any number k and any class of utility functions, the k -regret query outputs k tuples from the database and tries to minimize the maximum regret ratio . This captures how disappointed a user could be had she seen k representative tuples instead of the whole database. We focus on the class of linear utility functions, which is widely applicable. The first challenge of this approach is that it is not clear if the maximum regret ratio would be small, or even bounded. We answer this question affirmatively. Theoretically, we prove that the maximum regret ratio can be bounded and this bound is independent of the database size. Moreover, our extensive experiments on real and synthetic datasets suggest that in practice the maximum regret ratio is reasonably small. Additionally, algorithms developed in this paper are practical as they run in linear time in the size of the database and the experiments show that their running time is small when they run on top of the skyline operation which means that these algorithm could be integrated into current database systems.

Computing k-regret minimizing sets

“…• resolve a conjecture by Nanongkai et al [18], that finding 1-regret minimizing sets is an NP-hard problem, and extend the result for k-regret minimizing sets (Section 3);…”

“…A promising new alternative is the regret minimizing set, introduced by Nanongkai et al [18], which hybridizes the skyline operator with top-k queries. A top-k query takes as input a weight vector w and scores each point by inner product with w, reporting the k points with highest scores.…”

“…Motivated to derive a succinct representation of a dataset, one with fixed cardinality, Nanongkai et al introduce regret minimizing sets [18], 2 posing the question, "Does there exist one set of r points normalized points scores for given weight vectors id x y w0 = 1.00, 0.00 w1 = 0.72, 0.28 w2 = 0.52, 0.48 w3 = 0.32, 0.68 w4 = 0.00, = .14 .00 .00 .00 .23…”

Data driven approximation with bounded resources

“…Justification. Several accuracy measures have been studied for approximation, classified as (a) counting-based, e.g., Fmeasure and regret ratio [33]; (b) distance-based, e.g., Hausdorff distance [26] and MAC [27], using distance functions to measure either the gap between approximate and exact answers [27], or the "losslessness" of a synopsis; and (c) confidence probabilities for aggregate queries, e.g., BlinkDB [8] and sampling-based synopses [7,17]. However, they do not work well on resource-bounded approximation for generic queries, or do not give a deterministic accuracy.…”

“…We propose an RCmeasure for accuracy under the assumption that query relaxation [15,29] is allowed. As opposed to prior accuracy metrics [17,26,27,33], the RC measure assesses approximate answers in terms of both their relevance and coverage w.r.t. exact answers, and allows a deterministic accuracy lower bound for query answers computed by resource-bounded algorithms.…”