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

Authors:
Edward G. Thurber
Affiliations:
Department of Math and Computer Science, Biola University, 13800 Biola Avenue, LA Mirada, CA
Venue:
Discrete Mathematics
Year:
2002

Citing 3
Cited 1

The complexity of counting stable marriages

SIAM Journal on Computing
The stable marriage problem: structure and algorithms

The stable marriage problem: structure and algorithms
How do I marry thee? Let me count the ways

Discrete Applied Mathematics

A number of stable matchings in models of the Gale-Shapley type

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

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.