On testing substitutability

05/19/2018

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by   Cosmina Croitoru, et al.

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The papers hatfimmokomi11 and azizbrilharr13 propose algorithms for testing whether the choice function induced by a (strict) preference list of length N over a universe U is substitutable. The running time of these algorithms is O(|U|^3· N^3), respectively O(|U|^2· N^3). In this note we present an algorithm with running time O(|U|^2· N^2). Note that N may be exponential in the size |U| of the universe.