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- Benjamin Doerr, Daniel Johannsen, Carola Doerr
- Algorithmica
- 2010
Drift analysis is one of the strongest tools in the analysis of evolutionary algorithms. Its main weakness is that it is often very hard to find a good drift function.
In this paper, we make progress in this direction. We prove a multiplicative version of the classical drift theorem. This allows easier analyses in those settings, where the optimization… (More)
- Süntje Böttcher, Benjamin Doerr, Frank Neumann
- PPSN
- 2010
- Benjamin Doerr, Mahmoud Fouz, Tobias Friedrich
- Electronic Notes in Discrete Mathematics
- 2011
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)
- Benjamin Doerr, Leslie Ann Goldberg
- Algorithmica
- 2010
We show that, for any c>0, the (1+1) evolutionary algorithm using an arbitrary mutation rate p n =c/n finds the optimum of a linear objective function over bit strings of length n in expected time Θ(nlogn). Previously, this was only known for c≤1. Since previous work also shows that universal drift functions cannot exist for c larger than a certain… (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)
- Benjamin Doerr, Edda Happ, Christian Klein
- Theor. Comput. Sci.
- 2008
We show that the natural evolutionary algorithm for the all-pairs shortest path problem is significantly faster with a crossover operator than without. This is the first theoretical analysis proving the usefulness of crossover for a non-artificial problem.
- Benjamin Doerr, Daniel Johannsen, Carola Doerr
- IEEE Congress on Evolutionary Computation
- 2010
- Benjamin Doerr, Edda Happ, Christian Klein
- IEEE Congress on Evolutionary Computation
- 2007
— 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)
- Benjamin Doerr, Mahmoud Fouz, Carsten Witt
- GECCO
- 2011
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)
- Benjamin Doerr, Madeleine Theile
- GECCO
- 2009
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)