Efficient schemes for parallel communication
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
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We consider distributed computations in an asynchronous communication model with undetectable link failures. The computational tasks we consider are obtaining the value of a predetermined function of the local inputs scattered in the network (e.g., the sum of all local values). We call this task Global Computation.A trivial protocol for Global Computation consists of each processor sending its local input to all processors via flooding. Our aim is to justify the use of this simple protocol, in the presence of faulty links, by proving matching lower bounds on the message complexity (i.e., total number of messages sent) of Global Computation.In this paper we concentrate on the case in which the communication links are either unidirectional or fail in a uni-directional manner. Our main result states that for every n and m, the message complexity of Global Computation on such networks is at least n.m/PolyLog (n) where n is the number of processors and m is the number of links. Hence, in the presence of unidirectional link failures, the simple flooding algorithm is optimal up to a polylogarithmic factor.