Strong robustness of randomized rumor spreading protocols

Randomized rumor spreading is a classical protocol to disseminate information across a network. At SODA 2008, a quasirandom version of this protocol was proposed and competitive bounds for its run-time were proven. This prompts the question: to what extent does the quasirandom protocol inherit the second principal advantage of randomized rumor spreading, namely robustness against transmission failures?In this paper, we present a result precise up to (1±o(1))(1±o(1)) factors. We limit ourselves to the network in which the vertices form a clique. Run-times accurate to their leading constants are unknown for all other non-trivial networks.We show that if each transmission reaches its destination with probability p∈(0,1]p∈(0,1], after (1+ε)(1log2(1+p)log2n+1plnn) rounds where ε>0ε>0 is fixed, the quasirandom protocol has informed all nn nodes in the network with probability at least 1−n−pε/401−n−pε/40. Note that this is slightly faster than the intuitively natural 1/p1/p factor increase over the run-time of approximately log2n+lnnlog2n+lnn for the non-corrupted case.We also provide a corresponding lower bound for the classical model. This demonstrates that the quasirandom model is at least as robust as the fully random model despite the greatly reduced degree of independent randomness.