@article{Bredereck_Chen_Knop_Luo_Niedermeier_2020, title={Adapting Stable Matchings to Evolving Preferences}, volume={34}, url={https://ojs.aaai.org/index.php/AAAI/article/view/5550}, DOI={10.1609/aaai.v34i02.5550}, abstractNote={<p>Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing “incrementalized versions” of S<span style="font-variant: small-caps;">table</span> M<span style="font-variant: small-caps;">arriage</span> and S<span style="font-variant: small-caps;">table</span> R<span style="font-variant: small-caps;">oommates</span>. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of I<span style="font-variant: small-caps;">ncremental</span> S<span style="font-variant: small-caps;">table</span> M<span style="font-variant: small-caps;">arriage</span> and I<span style="font-variant: small-caps;">ncremental</span> S<span style="font-variant: small-caps;">table</span> R<span style="font-variant: small-caps;">oommates</span>. To this end, we exploit the parameters “degree of change” both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter “distance between old and new stable matching”.</p>}, number={02}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Bredereck, Robert and Chen, Jiehua and Knop, Dušan and Luo, Junjie and Niedermeier, Rolf}, year={2020}, month={Apr.}, pages={1830-1837} }