Adaptive Source Routing in High-Speed Networks

Appendix Proof of Lemma 1: The network topology implies, that any link emanating from s belongs to a single s-t path. The proof is by interchange argument: Since any path converging network is an sp graph, we use Theorem 1 to identify an optimal strategy with a unique order of trials on the network links. Assume that M (G) = (m 1 ; : : :; m n) is a complete order on paths for an optimal strategy S on G, then M (G) contains every s-t path in G. Let m i ; m i+1 be two consecutive elements in M (G), with the success probabilities p mi ; p mi+1 respectively, then it is suucient to show, that p mi < p mi+1 =) S is not optimal: Denote by Prob S (T > r) the probability, that for a given network, the number of trials of paths under the strategy S is higher than r, then We denote by S 0 the strategy, which switches m i and m i+1 , i.e. We handle the following two cases separately: