In this paper we consider the problem of computing an ''optimal'' popular matching. We assume that our input instance G = (A ∪ P , E 1∪ · · ·∪ E r ) admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness in which case we are required to return a fair popular matching. We show an O(n 2 + m) algorithm for this problem, assuming that the preference lists are strict, where m is the number of edges in G and n is the number of applicants.
Kavitha and Nasre REF described algorithms to determine an optimal popular matching for various interpretations of optimality.
Optimal popular matchings
Discret. Appl. Math.
Discret. Appl. Math.
Computer Science Mathematics