<p>Privacy preserving dynamic data publication aims at protecting data while simultaneously preserving its utility when the data is published dynamically. For static data (i.e., data published only once), privacy is based on concepts such as <i>k</i>-anonymity and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>-differential privacy. In contrast, for dynamic data, the notions of <i>m</i>-invariance and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-safety are considered. However, most current approaches focus solely on guaranteeing <i>m</i>-invariance and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-safety without paying attention to the quality of the solution, such as maximizing utility. We propose a new heuristic approach for the NP-hard combinatorial problem of <i>m</i>-invariance and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-safety, which is based on a mathematical optimization column generation scheme. The quality of a solution to <i>m</i>-invariance and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-safety can be measured by the Information Loss (<i>IL</i>), a value in [0, 100], the closer to 0 the better. We show that our approach improves by far current heuristics, reducing <i>IL</i> by more than <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(60\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>60</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> and, in some instances, by more than <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10514_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(95\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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A new mathematical optimization-based method for the m-invariance problem

  • Adrián Tobar Nicolau,
  • Jordi Castro,
  • Claudio Gentile

摘要

Privacy preserving dynamic data publication aims at protecting data while simultaneously preserving its utility when the data is published dynamically. For static data (i.e., data published only once), privacy is based on concepts such as k-anonymity and \(\epsilon \) ϵ -differential privacy. In contrast, for dynamic data, the notions of m-invariance and \(\tau \) τ -safety are considered. However, most current approaches focus solely on guaranteeing m-invariance and \(\tau \) τ -safety without paying attention to the quality of the solution, such as maximizing utility. We propose a new heuristic approach for the NP-hard combinatorial problem of m-invariance and \(\tau \) τ -safety, which is based on a mathematical optimization column generation scheme. The quality of a solution to m-invariance and \(\tau \) τ -safety can be measured by the Information Loss (IL), a value in [0, 100], the closer to 0 the better. We show that our approach improves by far current heuristics, reducing IL by more than \(60\%\) 60 % and, in some instances, by more than \(95\%\) 95 % .