Concerning the maximum number of stable matchings in the stable marriage problem
School of Science Technology and Health
The function, f(n), represents the maximum number of stable matchings possible in an instance of size n of the stable marriage problem. It is shown that f(n) is a strictly increasing function of n, and a result of Knuth's concerning the exponential growth of this function is generalized to apply to all positive integers, n. A method for constructing ranking matrices is used to produce instances with many stable matchings. A subproblem of the stable marriage problem developed by Eilers (Irvine Compiler Corporation Technical Report, ICC TR1999-2, 1999), called the pseudo-Latin marriage problem, plays a significant role as a tool and as motivation in the paper.
Stable marriage problem; Ranking matrix; Stable matchings
DOI of Published Version
Thurber, Edward G., "Concerning the maximum number of stable matchings in the stable marriage problem" (2002). Faculty Articles & Research. 640.