Adapting Stable Matchings to Evolving Preferences

Abstract

Adaptivity to changing environments and constraints is key to success in modern society. We address this view by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the 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 close to the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. 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, among the latter being one of the few fixed-parameter tractability results (exploiting the parameter "distance between old and new stable matching") in the context of computationally hard stable matching problems. * Supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement numbers 677651. † Supported by the DFG, project MaMu (NI 369/19). ‡ Supported by CAS-DAAD Joint Fellowship Program for Doctoral Students of UCAS. Work done while with TU Berlin. 1 The naming "Incremental" is inspired by work in the context of clustering and information retrieval [6].