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#### On Testing Substitutability

##### MPS-Authors
/persons/resource/persons44269

Croitoru,  Cosmina
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Fulltext (public)

arXiv:1805.07642.pdf
(Preprint), 69KB

##### Supplementary Material (public)
There is no public supplementary material available
##### Citation

Croitoru, C., & Mehlhorn, K. (2018). On Testing Substitutability. Retrieved from http://arxiv.org/abs/1805.07642.

Cite as: http://hdl.handle.net/21.11116/0000-0002-05FA-F
##### Abstract
The papers~\cite{hatfimmokomi11} and~\cite{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 $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that $N$ may be exponential in the size $|U|$ of the universe.