Title

Concerning the maximum number of stable matchings in the stable marriage problem

School/Department

School of Science Technology and Health

Publication Date

3-16-2002

Abstract

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.

Keywords

Stable marriage problem; Ranking matrix; Stable matchings

Publication Title

Discrete Mathematics

Volume

248

Issue

1-3

First Page

195

Last Page

2019

DOI of Published Version

10.1016/S0012-365X(01)00194-7

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