We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous distributed protocol while tolerating an optimal corruption of a @math fraction of all messages while incurring a moderate blowup of @math in the communication complexity. Our result is the first fully distributed interactive coding scheme in which the topology of the communication network is not known in advance. Prior work required either a coordinating node to be connected to all other nodes in the network or assumed a synchronous network in which all nodes already know the complete topology of the network.
@cite_35: Synchronizing distributed networks allows nodes to share resources efficiently, run synchronous programs and vote on redundant results in fault tolerant systems. Due to the low connectivity of hypercube networks, neither the fault tolerant hardware synchronization schemes, phased locked loops nor multistage synchronizers can be used without adding additional links. We describe a new hardware method developed to synchronize hypercube networks. Our analysis shows that the method can sustain one fault if the connectivity of the hypercube, n, is at least three, and it can tolerate up to m spl ges 2 Byzantine faults as long as the connectivity of the hypercube, n, is greater than max 2m+1,3m-2). This scheme has been implemented in an ASIC design for a hypercube of dimension five. It will be used in the Proteus parallel computer system to synchronize the circuit switching communication network. >
@cite_31: The computational power of different communication models is a fundamental question in the theory of distributed computation. For example, in the synchronous model messages are assumed to be delivered within one time unit, whereas in the asynchronous model message delays may be arbitrary. Another important parameter of the model is the assumptions about the topology. In the dynamic topology model, links are assumed to crash and recover dynamically, but their status is known to the incident node processors. A meaningful computation can be carried out if the topology stabilizes for a sufficiently long period. In this paper we show that the model of asynchronous, dynamic-topology network is equivalent, up to polylogarithmic factors, to the synchronous, static protocols that can withstand arbitrary link delays and changing topology at the expense of only polylogarithmic blowup in the running time, the number of messages, and the space requirement. Previous methods entailed a linear blowup in at least one of these resources. The generality of our method is demonstrated by a series of improvements for important applications, including Breadth First Search, computing compact efficient routing tables, and packet routing on asynchronous networks.
Synchronizers for unreliable settings have been studied by @cite_31 , which address a dynamic setting, and by Harrington and Somani @cite_35 , which assume faulty nodes.