k-Robust Single-Message Transmission
End-to-end communication considers the problem of sending messages between a sender s and a receiver r through an asynchronous, unreliable network, such as the Internet. We consider the problem of transmitting a single message from s to r through a network in which edges may fail and cannot recover. We assume that some s,r-path survives, but we do not know which path it is. A routing algorithm is k-robust if it ensures that a message sent by s will be received by r when at most k edges fail, and it will never generate an infinite number of messages. Graphs with a k-robust algorithm for all k were characterized in. For any other graph, its robustness is the maximum k for which it has a k-robust algorithm.
We provide general lower bounds for robustness by improving a natural algorithm obtained from Menger’s Theorem. We determine robustness for several examples, such as complete graphs, grids, and hypercubes.
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