Paper 2022/1173 Original: eprint.iacr.org/2022/1173 ↗

Secure Maximum Weight Matching Approximation on General Graphs (Full Version)

Abstract

Privacy-preserving protocols for matchings on general graphs can be used for applications such as online dating, bartering, or kidney donor exchange. In addition, they can act as a building blocks for more complex protocols. While privacy preserving protocols for matchings on bipartite graphs are a well-researched topic, the case of general graphs has experienced significantly less attention so far. We address this gap by providing the first privacy-preserving protocol for maximum weight matching on general graphs. We present two protocol variants, which both compute an $1/2-$approximation instead of an optimal solution in favor of scalability. For $N$ nodes, the first variant requires $\mathcal{O}(N \log^2 N)$ rounds and $\mathcal{O}(N^3\log N)$ communication, and the second variant requires only $\mathcal{O}(N \log N)$ rounds and $\mathcal{O}(N^3)$ communication. We implement both variants and find that the first variant runs in $14.9$ minutes for $N=300$ nodes, while the second variant requires only $5.1$ minutes for $N=300$, and $12.5$ minutes for $N=400$.