In the Seat Arrangement problem the goal is to allocate agents to vertices in a graph such that the resulting arrangement is optimal or fair in some way. Examples include an arrangement that maximises utility or one where no agent envies another. We introduce two new ways of calculating the utility that each agent derives from a given arrangement, one in which agents care only about their most preferred neighbour under a given arrangement, and another in which they only care about their least preferred neighbour. We also present a new restriction on agent's preferences, namely 1-dimensional preferences. We give algorithms, hardness results, and impossibility results for these new types of utilities and agents' preferences. Additionally, we refine previous complexity results, by showing that they hold in more restricted settings.

翻译：在座位安排问题中，目标是将智能体分配至图中的顶点，使得最终布局在某种意义下达到最优或公平。典型示例包括最大化整体效用的布局，或确保不存在智能体嫉妒其他智能体的布局。本文提出了两种计算智能体在给定布局下所获效用的新方法：一种仅考虑智能体在布局中最偏好的邻居，另一种仅考虑其最不偏好的邻居。同时，我们引入对智能体偏好的新约束条件——一维偏好。针对这些新型效用函数与智能体偏好，我们给出了相应算法、硬度证明与不可能性结果。此外，通过证明这些结果在更严格的约束条件下依然成立，我们对先前的计算复杂性结论进行了细化。