This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over so-called \emph{swaps}, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to $4/3$. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any $\varepsilon$, the trivial algorithm can\emph{not}\/ attain a $(2-\varepsilon)$-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than $2$.

翻译：本文研究基于条件偏好网络（CP-nets）表示的组合域偏好聚合问题的近似算法设计与分析。研究聚焦于所谓"交换"上的偏好聚合，已知此类问题的一般最优解具有指数规模。我们首先分析一个简单的2-近似算法（该算法仅输出输入偏好中的最优解），并建立了一个结构条件，使得该算法的近似比可改进至$4/3$。随后提出一种多项式时间近似算法，其输出结果理论上不劣于简单算法，且通常显著更优。通过构造一类问题实例，证明我们的改进算法可产生最优解，而简单算法对任意$\varepsilon$均无法达到$(2-\varepsilon)$的近似比。这些成果或可催生首个近似比显著优于2的多项式时间近似算法，用于求解交换上的CP-net聚合问题。