A Lower Bound for the Discrepancy of a Random Point Set

We show that there is a constant $K > 0$ such that for all $N, s \in \N$, $s \le N$, the point set consisting of $N$ points chosen uniformly at random in the $s$-dimensional unit cube $[0,1]^s$ with probability at least $1-\exp(-\Theta(s))$ admits an axis parallel rectangle $[0,x] \subseteq [0,1]^s$ containing $K \sqrt{sN}$ points more than expected. Consequently, the expected star discrepancy of a random point set is of order $\sqrt{s/N}$.Comment: 7 page

Improved Approximation Algorithms for the Min-Max Selecting Items Problem

We give a simple deterministic $O(\log K / \log\log K)$ approximation algorithm for the Min-Max Selecting Items problem, where $K$ is the number of scenarios. While our main goal is simplicity, this result also improves over the previous best approximation ratio of $O(\log K)$ due to Kasperski, Kurpisz, and Zieli\'nski (Information Processing Letters (2013)). Despite using the method of pessimistic estimators, the algorithm has a polynomial runtime also in the RAM model of computation. We also show that the LP formulation for this problem by Kasperski and Zieli\'nski (Annals of Operations Research (2009)), which is the basis for the previous work and ours, has an integrality gap of at least $\Omega(\log K / \log\log K)$

Simple and Optimal Randomized Fault-Tolerant Rumor Spreading

We revisit the classic problem of spreading a piece of information in a group of $n$ fully connected processors. By suitably adding a small dose of randomness to the protocol of Gasienic and Pelc (1996), we derive for the first time protocols that (i) use a linear number of messages, (ii) are correct even when an arbitrary number of adversarially chosen processors does not participate in the process, and (iii) with high probability have the asymptotically optimal runtime of $O(\log n)$ when at least an arbitrarily small constant fraction of the processors are working. In addition, our protocols do not require that the system is synchronized nor that all processors are simultaneously woken up at time zero, they are fully based on push-operations, and they do not need an a priori estimate on the number of failed nodes. Our protocols thus overcome the typical disadvantages of the two known approaches, algorithms based on random gossip (typically needing a large number of messages due to their unorganized nature) and algorithms based on fair workload splitting (which are either not {time-efficient} or require intricate preprocessing steps plus synchronization).Comment: This is the author-generated version of a paper which is to appear in Distributed Computing, Springer, DOI: 10.1007/s00446-014-0238-z It is available online from http://link.springer.com/article/10.1007/s00446-014-0238-z This version contains some new results (Section 6

Optimal Parameter Choices Through Self-Adjustment: Applying the 1/5-th Rule in Discrete Settings

While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the crossover rates of the algorithm. These parameters are known to have a crucial influence on the optimization time, and thus need to be chosen carefully, a task that often requires substantial efforts. Moreover, the optimal parameters can change during the optimization process. It is therefore of great interest to design mechanisms that dynamically choose best-possible parameters. An example for such an update mechanism is the one-fifth success rule for step-size adaption in evolutionary strategies. While in continuous domains this principle is well understood also from a mathematical point of view, no comparable theory is available for problems in discrete domains. In this work we show that the one-fifth success rule can be effective also in discrete settings. We regard the $(1+(\lambda,\lambda))$~GA proposed in [Doerr/Doerr/Ebel: From black-box complexity to designing new genetic algorithms, TCS 2015]. We prove that if its population size is chosen according to the one-fifth success rule then the expected optimization time on \textsc{OneMax} is linear. This is better than what \emph{any} static population size $\lambda$ can achieve and is asymptotically optimal also among all adaptive parameter choices.Comment: This is the full version of a paper that is to appear at GECCO 201

How European Protest Transforms Institutions of the Public Sphere - Discourse and Decision-Making in the European Social Forum Process

Against the background of the alleged democratic deficit of EU institutions, this case study explores how politicization and emerging transnational public spaces in European protest movements innovate existing practices of discursive or grassroots deliberative democracy in national social movements. I studied the European Social Forum (ESF) process, a transnational participatory democracy platform created by civil society groups and social movement organizations. I explored discourse and decision-making in the small-scale European Assemblies in which hundreds of activists have met six times a year since 2002 to organize the ESFs, and form campaigns on issues such as global and social justice, peace, climate change, migration, health, or education. Comparing activists’ democratic norms and discourse practices in these frequently occurring European Assemblies with social forum assemblies at the national level in Germany, Italy and the UK, I arrived at a surprising result: European Assemblies reflect a higher degree of discursive inclusivity, dialogue and transparency in decision-making and discussion compared to national social forum assemblies. In this paper I discuss structural, strategic and cultural changes that occur in the process of a Europeanization from below, that is, when social movement activists work together transnationally across a certain time period. I argue that European protest as a form of contentious Europeanization has developed new social practices and actors that innovate existing practices of participatory democracy at the national level, showing the relevance of social movements to democratize European integration.democracy; integration theory; democracy; European Public Sphere; Europeanization; Europeanization

Improved Protocols and Hardness Results for the Two-Player Cryptogenography Problem

The cryptogenography problem, introduced by Brody, Jakobsen, Scheder, and Winkler (ITCS 2014), is to collaboratively leak a piece of information known to only one member of a group (i)~without revealing who was the origin of this information and (ii)~without any private communication, neither during the process nor before. Despite several deep structural results, even the smallest case of leaking one bit of information present at one of two players is not well understood. Brody et al.\ gave a 2-round protocol enabling the two players to succeed with probability $1/3$ and showed the hardness result that no protocol can give a success probability of more than~$3/8$. In this work, we show that neither bound is tight. Our new hardness result, obtained by a different application of the concavity method used also in the previous work, states that a success probability better than 0.3672 is not possible. Using both theoretical and numerical approaches, we improve the lower bound to $0.3384$, that is, give a protocol leading to this success probability. To ease the design of new protocols, we prove an equivalent formulation of the cryptogenography problem as solitaire vector splitting game. Via an automated game tree search, we find good strategies for this game. We then translate the splits that occurred in this strategy into inequalities relating position values and use an LP solver to find an optimal solution for these inequalities. This gives slightly better game values, but more importantly, it gives a more compact representation of the protocol and a way to easily verify the claimed quality of the protocol. These improved bounds, as well as the large sizes and depths of the improved protocols we find, suggests that finding good protocols for the cryptogenography problem as well as understanding their structure are harder than what the simple problem formulation suggests