Control in Stable Marriage and Stable Roommates: Complexity and Algorithms

2025-02-03

AI Summary

This paper investigates “control problems” in stable matching settings: given agents with preference lists (e.g., for friendship or marriage), how can a central authority steer the system toward a desired matching via operations such as adding/deleting agents or modifying preference orders? We provide the first systematic complexity characterization of all major control variants in both the Stable Marriage and Stable Roommates models, fully classifying their computational hardness. Our results include multiple NP-hardness proofs and polynomial-time exact algorithms—some achieving optimal time complexity. Methodologically, we integrate combinatorial game modeling, parameterized complexity analysis, careful reduction constructions, and algorithmic design techniques including greedy strategies and dynamic programming. The work establishes a rigorous theoretical foundation for controllability in matching mechanisms and delivers practical algorithmic tools for mechanism design and policy intervention.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Mechanism Design
• Preference-based Choices
• Central Controller

Innovation

• Social Choice Theory
• Optimization Algorithms
• Preference Adjustment