Byzantine Stable Matching

2025-02-09

AI Summary

This paper investigates the stable matching problem in a distributed synchronous setting subject to Byzantine failures, where at most $t_L$ agents on the left side and $t_R$ agents on the right side may behave arbitrarily. We formally define the “Byzantine-tolerant stable matching” model and establish necessary and sufficient conditions for solvability. When both sides have equal cardinality and preferences are total orders, we show that solvability is fully determined by communication topology and cryptographic assumptions: without digital signatures, cross-side communication must be restricted; with signatures, significantly more permissive topologies become feasible. Our approach integrates distributed protocol design, Byzantine fault-tolerance theory, preference-order modeling, and secure communication mechanisms. The core contribution is a rigorous theoretical framework characterizing solvability, which reveals the fundamental role of cryptographic primitives—particularly digital signatures—in enhancing the fault tolerance of distributed stable matching.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Mechanism Design
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Applications of cryptography
• 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

Abstract

In stable matching, one must find a matching between two sets of agents, commonly men and women, or job applicants and job positions. Each agent has a preference ordering over who they want to be matched with. Moreover a matching is said to be stable if no pair of matched agents prefer each other compared to their current matching. We consider solving stable matching in a distributed synchronous setting, where each agent is its own process. Moreover, we assume up to $t_L$ agents on one side and $t_R$ on the other side can be byzantine. After properly defining the stable matching problem in this setting, we study its solvability. When there are as many agents on each side with fully-ordered preference lists, we give necessary and sufficient conditions for stable matching to be solvable in the synchronous setting. These conditions depend on the communication model used, i.e., if parties on the same side are allowed to communicate directly, and on the presence of a cryptographic setup, i.e., digital signatures.

Problem

• Byzantine agents in stable matching
• Distributed synchronous setting analysis
• Solvability conditions with communication models

Innovation

• Distributed synchronous stable matching
• Handles Byzantine fault tolerance
• Depends on communication, cryptographic setups