arXiv 2109.012052021-09-02cs.DC

有向超图中的拜占庭共识

Byzantine Consensus in Directed Hypergraphs

Muhammad Samir Khan, Nitin H. Vaidya

摘要：

拜占庭共识是分布式计算中的一个经典问题。同步系统中的每个节点都以二进制输入开始。我们的目标是在拜占庭故障节点的存在下达成协议。我们认为节点之间的通信是通过有向超图建模的设置。在经典的点对点通信模型中，节点之间的通信被建模为一个简单的图，其中在边缘上发送的所有消息在边缘的两个端点之间都是私有的。这允许有故障的节点模棱两可，即，对不同的邻居撒谎也不同在文献中已经提出了不同的模型，削弱模棱两可。在本地广播模型中，由节点发送的每个消息都被其所有邻居相同且正确地接收。在超图模型中，由超边上的节点发送的每个消息都被超边上的所有节点相同且正确地接收。对于无向（超）图的三种情况，紧网络条件是已知的。对于定向模型，已知点到点和本地广播模型的紧条件。在这项工作中，我们考虑的有向超图模型，包括所有上述模型。每个有向超边缘由单个头（发送者）和至少一个尾（接收者）组成，这模拟了本地多播信道，其中由发送者发送的消息被超边缘中的所有接收者相同地接收。对于这个模型，我们确定了达成共识的紧密网络条件。我们观察有向超图模型如何在特定条件下还原为上述三个模型中的每一个。在每种情况下，我们将网络条件与相应的已知紧条件联系起来。有向超图模型还包括其他感兴趣的实用网络模型，这些模型以前没有被探索过，如本文所述。

英文摘要：

Byzantine consensus is a classical problem in distributed computing. Each node in a synchronous system starts with a binary input. The goal is to reach agreement in the presence of Byzantine faulty nodes. We consider the setting where communication between nodes is modelled via a directed hypergraph. In the classical point-to-point communication model, the communication between nodes is modelled as a simple graph where all messages sent on an edge are private between the two endpoints of the edge. This allows a faulty node to equivocate, i.e., lie differently to its different neighbors. Different models have been proposed in the literature that weaken equivocation. In the local broadcast model, every message transmitted by a node is received identically and correctly by all of its neighbors. In the hypergraph model, every message transmitted by a node on a hyperedge is received identically and correctly by all nodes on the hyperedge. Tight network conditions are known for each of the three cases for undirected (hyper)graphs. For the directed models, tight conditions are known for the point-to-point and local broadcast models. In this work, we consider the directed hypergraph model that encompasses all the models above. Each directed hyperedge consists of a single head (sender) and at least one tail (receiver), This models a local multicast channel where messages transmitted by the sender are received identically by all the receivers in the hyperedge. For this model, we identify tight network conditions for consensus. We observe how the directed hypergraph model reduces to each of the three models above under specific conditions. In each case, we relate our network condition to the corresponding known tight conditions. The directed hypergraph model also encompasses other practical network models of interest that have not been explored previously, as elaborated in the paper.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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