  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.
