The Byzantine Brides Problem

TL;DR

This paper studies the difficulty of achieving stable marriages in a population with arbitrary initial states and malicious traitors, proving impossibility results and proposing an optimal protocol for traitor containment.

Contribution

It establishes the impossibility of fully traitor-insensitive solutions and introduces an optimal protocol for traitor containment in the stable marriage problem.

Findings

No fully traitor-insensitive solution exists.

Proposed protocol is optimal for traitor containment radius.

Demonstrates the impact of traitors on stability in marriage algorithms.

Abstract

We investigate the hardness of establishing as many stable marriages (that is, marriages that last forever) in a population whose memory is placed in some arbitrary state with respect to the considered problem, and where traitors try to jeopardize the whole process by behaving in a harmful manner. On the negative side, we demonstrate that no solution that is completely insensitive to traitors can exist, and we propose a protocol for the problem that is optimal with respect to the traitor containment radius.