Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems

08/02/2022
by   Niclas Boehmer, et al.
0

When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may become unstable. Then, a natural goal is to find a matching which is stable with respect to the modified preferences and as close as possible to the initial one. For Stable Marriage/Roommates, this problem was formally defined as Incremental Stable Marriage/Roommates by Bredereck et al. [AAAI '20]. As they showed that Incremental Stable Roommates and Incremental Stable Marriage with Ties are NP-hard, we focus on the parameterized complexity of these problems. We answer two open questions of Bredereck et al. [AAAI '20]: We show that Incremental Stable Roommates is W[1]-hard parameterized by the number of changes in the preferences, yet admits an intricate XP-algorithm, and we show that Incremental Stable Marriage with Ties is W[1]-hard parameterized by the number of ties. Furthermore, we analyze the influence of the degree of "similarity" between the agents' preference lists, identifying several polynomial-time solvable and fixed-parameter tractable cases, but also proving that Incremental Stable Roommates and Incremental Stable Marriage with Ties parameterized by the number of different preference lists are W[1]-hard.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/09/2020

Bribery and Control in Stable Marriage

We initiate the study of external manipulations in Stable Marriage by co...
05/16/2022

Stable Matching with Multilayer Approval Preferences: Approvals can be Harder than Strict Preferences

We study stable matching problems where agents have multilayer preferenc...
07/02/2019

Adapting Stable Matchings to Evolving Preferences

Adaptivity to changing environments and constraints is key to success in...
09/29/2020

Multidimensional Stable Roommates with Master List

Since the early days of research in algorithms and complexity, the compu...
08/19/2020

Stable Matchings with Restricted Preferences: Structure and Complexity

It is well known that every stable matching instance I has a rotation po...
11/21/2019

Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters

We continue and extend previous work on the parameterized complexity ana...
12/31/2021

Preference Swaps for the Stable Matching Problem

An instance I of the Stable Matching Problem (SMP) is given by a biparti...