### Abstract

In this paper, we consider the problem of testing substitutability of weak preferences. For this problem, Aziz, Brill, and Harrenstein proposed an O(ℓ
^{3}
u
^{2}
+ℓ
^{2}
u
^{2}
s
^{2}
)-time algorithm, where u is the size of the ground set, ℓ is the number of acceptable sets, and s is the maximum size of an equivalent class. In this paper, we propose an O(ℓ
^{3}
u+ℓ
^{2}
u
^{2}
s)-time algorithm for this problem. Our algorithm is based on a generalization of the characterization of substitutability of strict preferences given by Croitoru and Mehlhorn.

Original language | English |
---|---|

Pages (from-to) | 1-4 |

Number of pages | 4 |

Journal | Mathematical Social Sciences |

Volume | 99 |

DOIs | |

Publication status | Published - May 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Sociology and Political Science
- Social Sciences(all)
- Psychology(all)
- Statistics, Probability and Uncertainty

### Cite this

**An improved algorithm for testing substitutability of weak preferences.** / Kawanaka, Susumu; Kamiyama, Naoyuki.

Research output: Contribution to journal › Article

*Mathematical Social Sciences*, vol. 99, pp. 1-4. https://doi.org/10.1016/j.mathsocsci.2019.02.003

}

TY - JOUR

T1 - An improved algorithm for testing substitutability of weak preferences

AU - Kawanaka, Susumu

AU - Kamiyama, Naoyuki

PY - 2019/5/1

Y1 - 2019/5/1

N2 - In this paper, we consider the problem of testing substitutability of weak preferences. For this problem, Aziz, Brill, and Harrenstein proposed an O(ℓ 3 u 2 +ℓ 2 u 2 s 2 )-time algorithm, where u is the size of the ground set, ℓ is the number of acceptable sets, and s is the maximum size of an equivalent class. In this paper, we propose an O(ℓ 3 u+ℓ 2 u 2 s)-time algorithm for this problem. Our algorithm is based on a generalization of the characterization of substitutability of strict preferences given by Croitoru and Mehlhorn.

AB - In this paper, we consider the problem of testing substitutability of weak preferences. For this problem, Aziz, Brill, and Harrenstein proposed an O(ℓ 3 u 2 +ℓ 2 u 2 s 2 )-time algorithm, where u is the size of the ground set, ℓ is the number of acceptable sets, and s is the maximum size of an equivalent class. In this paper, we propose an O(ℓ 3 u+ℓ 2 u 2 s)-time algorithm for this problem. Our algorithm is based on a generalization of the characterization of substitutability of strict preferences given by Croitoru and Mehlhorn.

UR - http://www.scopus.com/inward/record.url?scp=85062870733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062870733&partnerID=8YFLogxK

U2 - 10.1016/j.mathsocsci.2019.02.003

DO - 10.1016/j.mathsocsci.2019.02.003

M3 - Article

VL - 99

SP - 1

EP - 4

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

ER -