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.
@InProceedings{cao_et_al:LIPIcs.ICDT.2017.11, author = {Cao, Wei and Li, Jian and Wang, Haitao and Wang, Kangning and Wang, Ruosong and Chi-Wing Wong, Raymond and Zhan, Wei}, title = {{k-Regret Minimizing Set: Efficient Algorithms and Hardness}}, booktitle = {20th International Conference on Database Theory (ICDT 2017)}, pages = {11:1--11:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-024-8}, ISSN = {1868-8969}, year = {2017}, volume = {68}, editor = {Benedikt, Michael and Orsi, Giorgio}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2017.11}, URN = {urn:nbn:de:0030-drops-70569}, doi = {10.4230/LIPIcs.ICDT.2017.11}, annote = {Keywords: multi-criteria decision-making, regret minimizing set, top-k query} }
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