The Fault-Tolerant Cluster-Sending Problem

[Solution] Byzantine Cluster-Sending in Expected Constant Cost and Constant Time

“…Before we present our probabilistic cluster-sending techniques, we first introduce all necessary terminology and notation. The formal model we use is based on the formalization of the cluster-sending problem provided by Hellings et al [18,20]. If S is a set of replicas, then f(S) ⊆ S denotes the faulty replicas in S, whereas nf(S) = S \ f(S) denotes the non-faulty replicas in S. We write n S = |S|, f S = |f(S)|, and nf S = |nf(S)| = n S −f S to denote the number of replicas, faulty replicas, and non-faulty replicas in S, respectively.…”

“…We note that the value v sent by cluster C 1 is a parameter of the cluster-sending problem. Typically, the value v originates from the resilient applications that are running on the clusters PBS-CS [18,20] min [18,20] n…”

“…Unfortunately, PCS does not guarantee termination, while PPCS has a worst-case quadratic complexity. In this section, we improve on this by presenting a probabilistic cluster-sending protocol that has expected constant cost and guarantees termination with a worst-case optimal linear complexity [18,20]. We refer to Table 1 for an overview of the notation used in this section.…”

“…1 Central to such complex system designs is the ability to reliably and efficiently communicate between independentlyoperating resilient clusters. Recently, this problem of communication between Byzantine fault-tolerant clusters has been formalized as the cluster-sending problem [18,20]. We believe that efficient solutions to this problem have a central role towards bridging resilient and high-performance data processing.…”

“…Although the cluster-sending problem has received some attention (e.g., as part of the design of AHL [7], BYSHARD [19,21], GEOBFT [16], and CHAINSPACE [1]), and clustersending protocols that solve the cluster-sending problem with worst-case optimal complexity are known [18,20], we believe there is still much room for improvement.…”