Three-Dimensional Popular Matching with Cyclic Preferences

TL;DR

This paper explores the relationship between stability and popularity in three-dimensional cyclic preference matchings, analyzing their properties and computational complexity under various conditions.

Contribution

It introduces a novel connection between popular matchings and three-dimensional cyclic preferences, extending the understanding of stability and popularity in complex matching scenarios.

Findings

Established links between stability and popularity in cyclic preferences

Analyzed the complexity of these problems with master list preferences

Derived new results on the strict variants of stability and popularity

Abstract

Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the input characteristics of the second one. We investigate the connection between stability, popularity, and their strict variants, strong stability and strong popularity in three-dimensional instances with cyclic preferences. Furthermore, we also derive results on the complexity of these problems when the preferences are derived from master lists.