7 research outputs found
k-Regret Minimizing Set: Efficient Algorithms and Hardness
We study the k-regret minimizing query (k-RMS), which is a useful operator for supporting multi-criteria decision-making. Given two integers k and r, a k-RMS returns r tuples from the database which minimize the k-regret ratio, defined as one minus the worst ratio between the k-th maximum utility score among all tuples in the database and the maximum utility score of the r tuples returned. A solution set contains only r tuples, enjoying the benefits of both top-k queries and skyline queries. Proposed in 2012, the query has been studied extensively in recent years. In this paper, we advance the theory and the practice of k-RMS in the following aspects. First, we develop efficient algorithms for k-RMS (and its decision version) when the dimensionality is 2. The running time of our algorithms outperforms those of previous ones. Second, we show that k-RMS is NP-hard even when the dimensionality is 3. This provides a complete characterization of the complexity of k-RMS, and answers an open question in previous studies. In addition, we present approximation algorithms for the problem when the dimensionality is 3 or larger
On Obtaining Stable Rankings
Decision making is challenging when there is more than one criterion to
consider. In such cases, it is common to assign a goodness score to each item
as a weighted sum of its attribute values and rank them accordingly. Clearly,
the ranking obtained depends on the weights used for this summation. Ideally,
one would want the ranked order not to change if the weights are changed
slightly. We call this property {\em stability} of the ranking. A consumer of a
ranked list may trust the ranking more if it has high stability. A producer of
a ranked list prefers to choose weights that result in a stable ranking, both
to earn the trust of potential consumers and because a stable ranking is
intrinsically likely to be more meaningful. In this paper, we develop a
framework that can be used to assess the stability of a provided ranking and to
obtain a stable ranking within an "acceptable" range of weight values (called
"the region of interest"). We address the case where the user cares about the
rank order of the entire set of items, and also the case where the user cares
only about the top- items. Using a geometric interpretation, we propose
algorithms that produce stable rankings. In addition to theoretical analyses,
we conduct extensive experiments on real datasets that validate our proposal