### Abstract

The concept of stable assignment comes from a classical assignment problem called the Stable Marriage Assignment. Suppose that there are two disjoint sets, one consists of men and the other of women. Each member of a set ranks the members of the other set in order of preference. Matching persons between two sets is a one-to-one relation. If there does not exist a random pair both preferring each other to their assigned partner, the assignment is said to be stable. In a recent paper. Huang and Chan generalized the above one-to-one type assignment problem to a multi-function assignment problem and proposed an algorithm for finding stable assignments for both problems. In this paper, we present a couterexample for which the assignment obtained by that algorithm is not stable.

Original language | English (US) |
---|---|

Pages (from-to) | 165-167 |

Number of pages | 3 |

Journal | International Journal of Computer Mathematics |

Volume | 41 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

### Fingerprint

### Keywords

- counterexample
- Stable assignment problem

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Applied Mathematics

### Cite this

*International Journal of Computer Mathematics*,

*41*(3-4), 165-167. https://doi.org/10.1080/00207169208804036

**On a new algorithm for stable assignment.** / Rosen, J. B.; Sun, S. Z.; Xue, Guoliang.

Research output: Contribution to journal › Article

*International Journal of Computer Mathematics*, vol. 41, no. 3-4, pp. 165-167. https://doi.org/10.1080/00207169208804036

}

TY - JOUR

T1 - On a new algorithm for stable assignment

AU - Rosen, J. B.

AU - Sun, S. Z.

AU - Xue, Guoliang

PY - 1992/1/1

Y1 - 1992/1/1

N2 - The concept of stable assignment comes from a classical assignment problem called the Stable Marriage Assignment. Suppose that there are two disjoint sets, one consists of men and the other of women. Each member of a set ranks the members of the other set in order of preference. Matching persons between two sets is a one-to-one relation. If there does not exist a random pair both preferring each other to their assigned partner, the assignment is said to be stable. In a recent paper. Huang and Chan generalized the above one-to-one type assignment problem to a multi-function assignment problem and proposed an algorithm for finding stable assignments for both problems. In this paper, we present a couterexample for which the assignment obtained by that algorithm is not stable.

AB - The concept of stable assignment comes from a classical assignment problem called the Stable Marriage Assignment. Suppose that there are two disjoint sets, one consists of men and the other of women. Each member of a set ranks the members of the other set in order of preference. Matching persons between two sets is a one-to-one relation. If there does not exist a random pair both preferring each other to their assigned partner, the assignment is said to be stable. In a recent paper. Huang and Chan generalized the above one-to-one type assignment problem to a multi-function assignment problem and proposed an algorithm for finding stable assignments for both problems. In this paper, we present a couterexample for which the assignment obtained by that algorithm is not stable.

KW - counterexample

KW - Stable assignment problem

UR - http://www.scopus.com/inward/record.url?scp=84885676856&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885676856&partnerID=8YFLogxK

U2 - 10.1080/00207169208804036

DO - 10.1080/00207169208804036

M3 - Article

AN - SCOPUS:84885676856

VL - 41

SP - 165

EP - 167

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 3-4

ER -