The ability of a peer-to-peer (P2P) system to effectively host decentralized applications often relies on the availability of a peer-sampling service, which provides each participant with a random sample of other peers. Despite the practical effectiveness of existing peer samplers, their ability to produce random samples within a reasonable time frame remains poorly understood from a theoretical standpoint. This paper contributes to bridging this gap by introducing PeerSwap, a peer-sampling protocol with provable randomness guarantees. We establish execution time bounds for PeerSwap, demonstrating its ability to scale effectively with the network size. We prove that PeerSwap maintains the fixed structure of the communication graph while allowing sequential peer position swaps within this graph. We do so by showing that PeerSwap is a specific instance of an interchange process, a renowned model for particle movement analysis. Leveraging this mapping, we derive execution time bounds, expressed as a function of the network size N. Depending on the network structure, this time can be as low as a polylogarithmic function of N, highlighting the efficiency of PeerSwap. We implement PeerSwap and conduct numerical evaluations using regular graphs with varying connectivity and containing up to 32768 (2^15) peers. Our evaluation demonstrates that PeerSwap quickly provides peers with uniform random samples of other peers.

翻译：点对点（P2P）系统有效承载去中心化应用的能力，通常依赖于对等节点采样服务的可用性，该服务为每个参与者提供其他节点的随机样本。尽管现有的对等节点采样器在实践中表现有效，但其在合理时间范围内生成随机样本的能力，从理论角度仍缺乏深入理解。本文通过引入PeerSwap这一具备可证明随机性保证的对等节点采样协议，致力于弥合这一理论空白。我们建立了PeerSwap的执行时间界限，证明其能够随网络规模有效扩展。我们证明了PeerSwap在保持通信图固定结构的同时，允许在该图中进行顺序化的节点位置交换。这一结论通过将PeerSwap构建为互换过程（一种用于分析粒子运动的经典模型）的特例而得以证明。借助该映射关系，我们推导出以网络规模N为函数的执行时间界限。根据网络结构的不同，该时间可低至N的多对数函数，这突显了PeerSwap的高效性。我们实现了PeerSwap协议，并采用具有不同连通度、最多包含32768（2^15）个节点的正则图进行了数值评估。实验结果表明，PeerSwap能够快速为节点提供均匀随机的其他节点样本。