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Segala. Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, Dept. of Electrical Engineering and Computer Science, 1995. Also appears as technical report MIT/LCS/TR-676. A Simple DFS-Based Algorithm for Linear Interval Routing T. Eilam, S. Moran*, S. technion. il A b s t r a c t . Linear Interval Routing is a space-efficient routing method tbr point-to-point communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wrap-around.

H, O] < ( K + 1)2n ~ + n. L e m m a 18. Let H be a probabilistic execution fragment of DAH that starts from a reachable state, and let 0 be a full cut of H. Then E~,,,,r[H , O] <_ (K + 1)2n'~ + 2n. L e m m a 19. max-round. Suppose that s is reachable. Let 0 denote the set of minimal states of H where a state from 7) is reached. Then E~,,,[H, O] = O(Rn2). The main result is just a pasting together of the results obtained so far. An immediate consequence on the algorithm of Aspnes and Herlihy is that, if we know that some initialized process does not fail and that the maximum round is 1, then a decision is reached within expected cubic time.

D get only response v, then a state f r o m D is reached within two rounds. 2 Probabilistic Progress Properties Suppose that each coin flipping protocol CFr satisfies the following properties. C 1 For each fairprobabilisticexecution fragment of CFr that startswith a reachable state of CFr, the probability that each invocation on a non-failingport gets a response is 1. C 2 For each fair probabilisticexecution of CFr, and each value v E {0, 1}, the probability that all invocations on a non-failingport get response v is at leastp, O

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