Seat Arrangement Problems under B-utility and W-utility

TL;DR

This paper introduces novel utility models and preference restrictions for seat arrangement problems, providing algorithms, complexity, and impossibility results to improve understanding of fair and optimal allocations.

Contribution

It presents new utility calculation methods, preference restrictions, and extends complexity results for seat arrangement problems.

Findings

New utility models based on most and least preferred neighbors

Algorithms and hardness results for these utility models

Refined complexity results under restricted preferences

Abstract

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.