Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing feasible solutions to this integer program, and use it to prove an upper bound for permutation resemblance for some special functions. Additionally, we present a generalization of the linear integer program that takes a function on a finite group and determines a permutation with the lowest differential uniformity among those most resembling it.

翻译：置换相似性用于衡量函数与置换函数之间的偏离程度。本文通过线性整数规划方法展示了如何确定置换相似性。同时提出了一种构造该整数规划可行解的算法，并利用该算法证明了若干特殊函数置换相似性的上界。此外，给出线性整数规划的推广形式，该规划可对有限群上的函数进行处理，并在与其最相似的置换中确定微分均匀性最低的置换。