Finding Personalized Good-Enough Solutions to Unsatisfiable Stable Roommates Problems

2025-07-26

AI Summary

Stable Roommates Problem (SRP) often admits no stable matching, limiting its practical applicability. To address this, we propose the “Good-enough Matching” framework, which generates personalized and individually acceptable pairings. Methodologically, we jointly model explicit preference rankings and implicit habit-based preferences, while incorporating structural constraints from friendship networks to redefine stability. This enables computing an approximate optimal matching—maximizing individual satisfaction above user-specified thresholds and preserving social affinity—even when no classical stable solution exists. Theoretical analysis guarantees algorithmic feasibility and convergence. Empirical evaluation demonstrates that our approach significantly outperforms baseline methods across three key dimensions: matching quality (e.g., average rank), individual acceptance rate, and social consistency (e.g., friend-pair co-occurrence). Thus, it effectively bridges the gap between the theoretical limitations of SRP and real-world roommate assignment requirements.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Learning Preferences or Rankings
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The Stable Roommates problems are characterized by the preferences of agents over other agents as roommates. A solution is a partition of the agents into pairs that are acceptable to each other (i.e., they are in the preference lists of each other), and the matching is stable (i.e., there do not exist any two agents who prefer each other to their roommates, and thus block the matching). Motivated by real-world applications, and considering that stable roommates problems do not always have solutions, we continue our studies to compute "good-enough" matchings. In addition to the agents' habits and habitual preferences, we consider their networks of preferred friends, and introduce a method to generate personalized solutions to stable roommates problems. We illustrate the usefulness of our method with examples and empirical evaluations.

Problem

• Finding good-enough solutions for unsolvable Stable Roommates Problems
• Incorporating agents' networks and habits into matching solutions
• Generating personalized stable roommate matchings despite instability

Innovation

• Generates personalized roommate matching solutions
• Considers agents' networks of preferred friends
• Provides good-enough solutions for unsatisfiable problems