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DOI: 10.4230/LIPIcs.ICDT.2017.11
k-Regret Minimizing Set: Efficient Algorithms and Hardness

Authors: Wei Cao, Jian Li, Haitao Wang, Kangning Wang, Ruosong Wang, Raymond Chi-Wing Wong, and Wei Zhan

Published in: LIPIcs, Volume 68, 20th International Conference on Database Theory (ICDT 2017)

Abstract
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.
Cite as

Wei Cao, Jian Li, Haitao Wang, Kangning Wang, Ruosong Wang, Raymond Chi-Wing Wong, and Wei Zhan. k-Regret Minimizing Set: Efficient Algorithms and Hardness. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@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-dev.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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