One of the fundamental problems in distributed computing is how to efficiently perform routing in a faulty network in which each link fails with some probability. This paper investigates how big the failure probability can be, before the capability to efficiently find a path in the network is lost. The main results show tight upper and lower bounds for the failure probability which permits routing, both for the hypercube and for the d-dimensional mesh. The authors use tools from percolation theory to show that in the d-dimensional mesh, once a giant component appears - efficient routing is possible. A different behavior is observed when the hypercube is considered.
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