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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)
Jim Propp's P-machine, also known as the 'rotor router model' is a simple deterministic process that simulates a random walk on a graph. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order. We investigate how well this process simulates a random walk. For the graph being the infinite path, we show that,(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 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)
The runtime analysis of randomized search heuristics is a growing field where, in the last two decades, many rigorous results have been obtained. These results, however, apply particularly to classical search heuristics such as Evolutionary Algorithms (EAs) and Simulated Annealing. First runtime analyses of modern search heuristics have been conducted only(More)