Control in Stable Marriage and Stable Roommates: Complexity and Algorithms
Jiehua Chen, Ildikó Schlotter
TL;DR
The paper investigates how a controller can influence Stable Marriage and Stable Roommates instances through actions that add or delete agents or delete acceptability, aiming to achieve goals such as ensuring a specific agent or pair is matched, or guaranteeing the existence of a stable/perfect matching. It delivers a complete complexity landscape by presenting NP-completeness results for several AddAg-based goals (notably making an agent or a pair matchable and achieving a perfect stable matching in some cases) and polynomial-time algorithms for several DelAg and DelAcc variants (including MP/MA and MS-related goals). The authors employ reductions from Clique and Independent Set to establish hardness and leverage stable partitions and existing results to design efficient algorithms for deletion-based control. Collectively, the work clarifies the computational boundaries of manipulation/control in matching with preferences, offering guidance for designing robust matching systems and identifying where automated control is computationally feasible or intractable. The findings have implications for understanding resilience and vulnerability of matching markets under external interventions.
Abstract
We study control problems in the context of matching under preferences: We examine how a central authority, called the controller, can manipulate an instance of the Stable Marriage or Stable Roommates problems in order to achieve certain goals. We investigate the computational complexity of the emerging problems, and provide both efficient algorithms and intractability results.