On Byzantine Agreement over (2, 3)-Uniform Hypergraphs

In a Byzantine agreement protocol, a synchronous network of n interconnected processes of which t may be faulty, starts with an initial binary value associated with each process; after exchanging messages, all correct processes must agree on one of the initial values of the non-faulty processes. If the network consists of only unicast channels (i.e. a 2-uniform hypergraph), then Byzantine agreement is possible if and only if n ≥ 3t + 1 (Pease et. al. [11]). However, Fitzi and Maurer ([7]) show that if, in addition to all unicast channels, there exists local broadcast among every three processes in the network (i.e. a complete (2, 3)-uniform hypergraph), n ≥ 2t + 1 is necessary and sufficient for Byzantine agreement. In this paper, we show that optimum tolerance of n ≥ 2t + 1 can be achieved even if a substantial fraction of the local broadcast channels are not available. Specifically, we model the network as a (2, 3)-uniform hypergraph H = (P, E), where P denotes the set of n pr...

• Type: Conference
• Year: 2004
• Where: WDAG
• Authors: D. V. S. Ravikant, Muthuramakrishnan Venkitasubramaniam, V. Srikanth, K. Srinathan, C. Pandu Rangan
• Keywords: Algorithms, Byzantine Agreement, Byzantine Agreement Protocol, Unicast Channels, WDAG 2004