Privacy-preserving data splitting is a technique that aims to protect data privacy by storing different fragments of data in different locations. In this work we give a new combinatorial formulation to the data splitting problem. We see the data splitting problem as a purely combinatorial problem, in which we have to split data attributes into different fragments in a way that satisfies certain combinatorial properties derived from processing and privacy constraints. Using this formulation, we develop new combinatorial and algebraic techniques to obtain solutions to the data splitting problem. We present an algebraic method which builds an optimal data splitting solution by using Gröbner bases. Since this method is not efficient in general, we also develop a greedy algorithm for finding solutions that are not necessarily minimally sized.

隐私保护数据拆分是一项旨在通过在不同位置存储不同数据片段来保护数据隐私的技术。在这项工作中，我们对数据分割问题给出了新的组合表述。我们将数据拆分问题视为纯粹的组合问题，其中我们必须以满足从处理和隐私约束得出的某些组合属性的方式，将数据属性拆分为不同的片段。使用此公式，我们开发了新的组合和代数技术来获取数据拆分问题的解决方案。我们提出了一种代数方法，该方法通过使用Gröbner基建立了最佳的数据拆分解决方案。由于此方法通常效率不高，因此我们还开发了一种贪婪算法，用于查找不一定需要最小尺寸的解决方案。