# Faster approximation algorithm for the k-Regret minimizing set and related problems

## Abstract

Efficient multi-criteria decision making often requires looking at a small set of representative objects from a large collection. A recently proposed method for finding representative objects is the k-regret minimizing set (k- RMS problem). Intuitively, given a large set of objects (points) in d dimensions, the goal is to choose a small representative subset, such that for every user preference, there is always an object in the subset whose preference score is not much worse than the score of the k-th most preferred object in the original set. We propose two new efficient approximation algorithms for the k-regret minimizing set problem with provable theoretical guarantees. Our algorithms improve on the space and time complexities of previous approximation algorithms for the k- RMS problem. In addition, we run extensive experiments on real and synthetic data sets showing that simple modifications of our theoretical algorithms run significantly faster than the previous implementations of the k- RMS problem. Finally, we present an efficient approximation algorithm with theoretical guarantees for an extension of the k- RMS problem, which is called the Top-k regret minimizing set problem.

## Publication Title

Proceedings of the Workshop on Algorithm Engineering and Experiments

## Recommended Citation

Kumar, N., & Sintos, S.
(2018). Faster approximation algorithm for the k-Regret minimizing set and related problems.* Proceedings of the Workshop on Algorithm Engineering and Experiments**, 2018-January*, 62-74.
https://doi.org/10.1137/1.9781611975055.6