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.
All Science Journal Classification (ASJC) codes
- Sociology and Political Science
- Social Sciences(all)
- Statistics, Probability and Uncertainty