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DOI: 10.4230/LIPIcs.ICDT.2022.7

Improved Approximation and Scalability for Fair Max-Min Diversification

Authors: Raghavendra Addanki, Andrew McGregor, Alexandra Meliou, and Zafeiria Moumoulidou

Published in: LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Abstract

Given an n-point metric space ({𝒳},d) where each point belongs to one of m = O(1) different categories or groups and a set of integers k₁, …, k_m, the fair Max-Min diversification problem is to select k_i points belonging to category i ∈ [m], such that the minimum pairwise distance between selected points is maximized. The problem was introduced by Moumoulidou et al. [ICDT 2021] and is motivated by the need to down-sample large data sets in various applications so that the derived sample achieves a balance over diversity, i.e., the minimum distance between a pair of selected points, and fairness, i.e., ensuring enough points of each category are included. We prove the following results: 1) We first consider general metric spaces. We present a randomized polynomial time algorithm that returns a factor 2-approximation to the diversity but only satisfies the fairness constraints in expectation. Building upon this result, we present a 6-approximation that is guaranteed to satisfy the fairness constraints up to a factor 1-ε for any constant ε. We also present a linear time algorithm returning an m+1 approximation with exact fairness. The best previous result was a 3m-1 approximation. 2) We then focus on Euclidean metrics. We first show that the problem can be solved exactly in one dimension. {For constant dimensions, categories and any constant ε > 0, we present a 1+ε approximation algorithm that runs in O(nk) + 2^{O(k)} time where k = k₁+…+k_m.} We can improve the running time to O(nk)+poly(k) at the expense of only picking (1-ε) k_i points from category i ∈ [m]. Finally, we present algorithms suitable to processing massive data sets including single-pass data stream algorithms and composable coresets for the distributed processing.

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Raghavendra Addanki, Andrew McGregor, Alexandra Meliou, and Zafeiria Moumoulidou. Improved Approximation and Scalability for Fair Max-Min Diversification. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{addanki_et_al:LIPIcs.ICDT.2022.7,
  author =	{Addanki, Raghavendra and McGregor, Andrew and Meliou, Alexandra and Moumoulidou, Zafeiria},
  title =	{{Improved Approximation and Scalability for Fair Max-Min Diversification}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-223-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{220},
  editor =	{Olteanu, Dan and Vortmeier, Nils},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.7},
  URN =		{urn:nbn:de:0030-drops-158812},
  doi =		{10.4230/LIPIcs.ICDT.2022.7},
  annote =	{Keywords: algorithmic fairness, diversity maximization, data selection, approximation algorithms}
}

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DOI: 10.4230/LIPIcs.ICDT.2021.13

Diverse Data Selection under Fairness Constraints

Authors: Zafeiria Moumoulidou, Andrew McGregor, and Alexandra Meliou

Published in: LIPIcs, Volume 186, 24th International Conference on Database Theory (ICDT 2021)

Abstract

Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer the first study that augments the Max-Min diversification objective with fairness constraints. More specifically, given a universe 𝒰 of n elements that can be partitioned into m disjoint groups, we aim to retrieve a k-sized subset that maximizes the pairwise minimum distance within the set (diversity) and contains a pre-specified k_i number of elements from each group i (fairness). We show that this problem is NP-complete even in metric spaces, and we propose three novel algorithms, linear in n, that provide strong theoretical approximation guarantees for different values of m and k. Finally, we extend our algorithms and analysis to the case where groups can be overlapping.

Cite as

Zafeiria Moumoulidou, Andrew McGregor, and Alexandra Meliou. Diverse Data Selection under Fairness Constraints. In 24th International Conference on Database Theory (ICDT 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 186, pp. 13:1-13:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{moumoulidou_et_al:LIPIcs.ICDT.2021.13,
  author =	{Moumoulidou, Zafeiria and McGregor, Andrew and Meliou, Alexandra},
  title =	{{Diverse Data Selection under Fairness Constraints}},
  booktitle =	{24th International Conference on Database Theory (ICDT 2021)},
  pages =	{13:1--13:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-179-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{186},
  editor =	{Yi, Ke and Wei, Zhewei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2021.13},
  URN =		{urn:nbn:de:0030-drops-137216},
  doi =		{10.4230/LIPIcs.ICDT.2021.13},
  annote =	{Keywords: data selection, diversity maximization, fairness constraints, approximation algorithms}
}

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Improved Approximation and Scalability for Fair Max-Min Diversification

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Diverse Data Selection under Fairness Constraints

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