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With the prevalence of social networks, it has become increasingly important to understand their features and limitations. It has been observed that information spreads extremely fast in social networks. We study the performance of randomized rumor spreading protocols on graphs in the preferential attachment model. The well-known random phone call model of(More)
In the standard consensus problem there are <i>n</i> processes with possibly different input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the <i>stabilizing consensus problem</i> [2]. In this problem, we do not require that(More)
— We conduct a rigorous analysis of the (1 + 1) evolutionary algorithm for the single source shortest path problem proposed by Scharnow, Tinnefeld and Wegener (Journal of Mathematical Modelling and Algorithms, 2004). We prove a tight bound of Θ(n 2 max{log(n), ℓ}) on the optimization time, where ℓ is the maximum number of edges of a shortest path with(More)
We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al. (GECCO~2010) in several respects. First, the upper bound on the(More)
We deepen the theoretical analysis of the genetic algorithm for the all-pairs shortest path problem proposed by Doerr, Happ and Klein (GECCO 2008). We show that the growth of the paths through crossover operations can be analyzed without the previously used approach of waiting until all paths of a certain length are present in the population. This allows to(More)