A Peer-to-Peer (P2P) network is a dynamic collection of nodes that connect with each other via virtual overlay links built upon an underlying network (usually, the Internet). P2P networks are highly dynamic and can experience very heavy churn, i.e., a large number of nodes join/leave the network continuously. Thus, building and maintaining a stable overlay network is an important problem that has been studied extensively for two decades.

In this paper, we present our P2P overlay network called Sparse Robust Addressable Network (Spartan). Spartan can be quickly and efficiently built in a fully distributed fashion within $O(logn)$ rounds. Furthermore, the Spartan overlay structure can be maintained, again, in a fully distributed manner despite adversarially controlled churn (i.e., nodes joining and leaving) and significant variation in the number of nodes. Moreover, new nodes can join a committee within $O\left(1\right)$ rounds and leaving nodes can leave without any notice.

The number of nodes in the network lies in $[n,fn]$ for any fixed $f\ge 1$. Up to $ϵn$ nodes (for some small but fixed $ϵ>0$) can be adversarially added/deleted within any period of $P$ rounds for some $P\in O(loglogn)$. Despite such uncertainty in the network, Spartan maintains $\Theta (n∕logn)$ committees that are stable and addressable collections of $\Theta (logn)$ nodes each for $\text{polynomial}\left(n\right)$ rounds with high probability.

Spartan’s committees are also capable of performing sustained computation and passing messages between each other. Thus, any protocol designed for static networks can be simulated on Spartan with minimal overhead. This makes Spartan an ideal platform for developing applications. We experimentally show that Spartan will remain robust as long as each committee, on average, contains 24 nodes for networks of size up to 10240.

对等（P2P）网络是节点的动态集合，这些节点通过基于基础网络（通常是Internet）构建的虚拟覆盖链接相互连接。P2P网络是高度动态的，并且会遭受很大的用户流失，即，大量节点连续加入/离开网络。因此，建立和维护一个稳定的覆盖网络是一个已经研究了二十年的重要问题。

在本文中，我们介绍了称为稀疏健壮可寻址网络（Spartan）的P2P覆盖网络。可以在内部以完全分布式的方式快速有效地构建Spartan$Ø（日志ñ）$回合。此外，尽管有对抗控制的搅动（即，节点加入和离开）以及节点数量的显着变化，但仍可以以完全分布式的方式来维持Spartan覆盖结构。此外，新节点可以加入内部的委员会$Ø（\mathrm{1个}）$ 回合和离开节点可以离开而无需任何通知。

网络中的节点数位于 $[ñ，Fñ]$ 对于任何固定 $F\ge \mathrm{1个}$。取决于$ϵñ$ 节点（对于一些小的但固定的 $ϵ>0$）可以在任何时间段内进行对抗性添加/删除$P$ 为一些回合 $P\in Ø（日志日志ñ）$。尽管网络存在不确定性，但Spartan认为$\Theta （ñ∕日志ñ）$ 稳定且可寻址的集合的委员会 $\Theta （日志ñ）$ 每个节点 $\text{多项式}（ñ）$ 几率很高。

Spartan的委员会还能够执行持续的计算并在彼此之间传递消息。因此，可以在Spartan上以最小的开销模拟为静态网络设计的任何协议。这使Spartan成为开发应用程序的理想平台。我们通过实验表明，只要每个委员会平均包含24个节点，网络规模最大为10240，Spartan就会保持强大。