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DOI: 10.4230/LIPIcs.ITCS.2024.23

Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine

Authors: Clément L. Canonne and Yucheng Sun

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract

Private closeness testing asks to decide whether the underlying probability distributions of two sensitive datasets are identical or differ significantly in statistical distance, while guaranteeing (differential) privacy of the data. As in most (if not all) distribution testing questions studied under privacy constraints, however, previous work assumes that the two datasets are equally sensitive, i.e., must be provided the same privacy guarantees. This is often an unrealistic assumption, as different sources of data come with different privacy requirements; as a result, known closeness testing algorithms might be unnecessarily conservative, "paying" too high a privacy budget for half of the data. In this work, we initiate the study of the closeness testing problem under heterogeneous privacy constraints, where the two datasets come with distinct privacy requirements. We formalize the question and provide algorithms under the three most widely used differential privacy settings, with a particular focus on the local and shuffle models of privacy; and show that one can indeed achieve better sample efficiency when taking into account the two different "epsilon" requirements.

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Clément L. Canonne and Yucheng Sun. Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{canonne_et_al:LIPIcs.ITCS.2024.23,
  author =	{Canonne, Cl\'{e}ment L. and Sun, Yucheng},
  title =	{{Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{23:1--23:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.23},
  URN =		{urn:nbn:de:0030-drops-195518},
  doi =		{10.4230/LIPIcs.ITCS.2024.23},
  annote =	{Keywords: differential privacy, distribution testing, local privacy, shuffle privacy}
}

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DOI: 10.4230/LIPIcs.ESA.2023.99

The Tight Spanning Ratio of the Rectangle Delaunay Triangulation

Authors: André van Renssen, Yuan Sha, Yucheng Sun, and Sampson Wong

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract

Spanner construction is a well-studied problem and Delaunay triangulations are among the most popular spanners. Tight bounds are known if the Delaunay triangulation is constructed using an equilateral triangle, a square, or a regular hexagon. However, all other shapes have remained elusive. In this paper we extend the restricted class of spanners for which tight bounds are known. We prove that Delaunay triangulations constructed using rectangles with aspect ratio A have spanning ratio at most √2 √{1+A² + A √{A²+1}}, which matches the known lower bound.

Cite as

André van Renssen, Yuan Sha, Yucheng Sun, and Sampson Wong. The Tight Spanning Ratio of the Rectangle Delaunay Triangulation. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 99:1-99:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vanrenssen_et_al:LIPIcs.ESA.2023.99,
  author =	{van Renssen, Andr\'{e} and Sha, Yuan and Sun, Yucheng and Wong, Sampson},
  title =	{{The Tight Spanning Ratio of the Rectangle Delaunay Triangulation}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{99:1--99:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.99},
  URN =		{urn:nbn:de:0030-drops-187523},
  doi =		{10.4230/LIPIcs.ESA.2023.99},
  annote =	{Keywords: Spanners, Delaunay Triangulation, Spanning Ratio}
}

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Documents authored by Sun, Yucheng

Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine

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The Tight Spanning Ratio of the Rectangle Delaunay Triangulation

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