Investigation of algorithms for variants of the Stable Matching Problem

The purpose of this study is to explore and provide alternative algorithms for three variants of the stable matching problem. The Stable Matching Problem is to find a matching between two groups, where both group members list their preferences by rating the opposite group members. A matching consists of two individuals of different groups all of whom regard themselves as married to each other. The goal of this study is the analysis of three variants of the stable matching problem by providing algorithms for each of the variant. Variants of the Stable Matching Problem that are explored in this paper are: Stable Matching with Forbidden Pairs, Stable Matching with Incomplete Preference Lists, and Stable Matching with Polygamous Partners.Two algorithms will be designed for each variant of the Stable Matching problem.These algorithms will then be analyzed for time, overall unhappiness, and the number of instabilities. The two algorithms for one variant will be competing against each other for time efficiency, number of stable pairs and overall happiness. A user interface will be built to recognize which algorithm is preferable for each variant depending on the chosen criteria and size.