A Novel Graph-Based Algorithm for Solving the Right Partner Problem

In this research, the right partner problem is investigated and a new polynomial graph-based algorithm to solve it is proposed. The right partner problem belongs to the category of well-known assignment and matching problems. In the right partner problem, groups of persons are formed within one set, while in the assignment and matching problems, elements from two different sets are linked together. The authors propose modeling the problem using graphs with special weights on edges and nodes. In this paper, the authors applied and illustrated the developed algorithm to solve a real life instance of the problem by creating pairs from a given set of n students. The solution is based on student choices of like and dislike relationships with other students and aims to maximize the degree of overall satisfaction of students' preferences.