Petra Berenbrink
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View article: (Almost) Perfect Discrete Iterative Load Balancing
(Almost) Perfect Discrete Iterative Load Balancing Open
We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually eac…
View article: A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols
A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols Open
View article: A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols
A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols Open
We consider the problem of self-stabilizing leader election in the population model by Angluin, Aspnes, Diamadi, Fischer, and Peralta (JDistComp '06). The population model is a well-established and powerful model for asynchronous, distribu…
View article: Silent Self-Stabilizing Ranking: Time Optimal and Space Efficient
Silent Self-Stabilizing Ranking: Time Optimal and Space Efficient Open
We present a silent, self-stabilizing ranking protocol for the population protocol model of distributed computing, where agents interact in randomly chosen pairs to solve a common task. We are given $n$ anonymous agents, and the goal is to…
View article: WalkSAT is linear on random 2-SAT
WalkSAT is linear on random 2-SAT Open
In an influential article Papadimitriou [FOCS 1991] proved that a local search algorithm called WalkSAT finds a satisfying assignment of a satisfiable 2-CNF with $n$ variables in $O(n^2)$ expected time. Variants of the WalkSAT algorithm ha…
View article: Undecided State Dynamics with Stubborn Agents
Undecided State Dynamics with Stubborn Agents Open
In the classical Approximate Majority problem with two opinions there are agents with Opinion 1 and with Opinion 2. The goal is to reach consensus and to agree on the majority opinion if the bias is sufficiently large. It is well known tha…
View article: Asynchronous opinion dynamics in social networks
Asynchronous opinion dynamics in social networks Open
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. A prominent model to study opinion formation processes is due to Hegselmann and Krause. It has the dist…
View article: Population Protocols for Exact Plurality Consensus -- How a small chance of failure helps to eliminate insignificant opinions
Population Protocols for Exact Plurality Consensus -- How a small chance of failure helps to eliminate insignificant opinions Open
We consider the \emph{exact plurality consensus} problem for \emph{population protocols}. Here, $n$ anonymous agents start each with one of $k$ opinions. Their goal is to agree on the initially most frequent opinion (the \emph{plurality op…
View article: Fast Convergence of $k$-Opinion Undecided State Dynamics in the Population Protocol Model
Fast Convergence of $k$-Opinion Undecided State Dynamics in the Population Protocol Model Open
We analyze the convergence of the $k$-opinion Undecided State Dynamics (USD) in the population protocol model. For $k$=2 opinions it is well known that the USD reaches consensus with high probability within $O(n \log n)$ interactions. Prov…
View article: Barriers for Faster Dimensionality Reduction
Barriers for Faster Dimensionality Reduction Open
The Johnson-Lindenstrauss transform allows one to embed a dataset of n points in ℝ^d into ℝ^m, while preserving the pairwise distance between any pair of points up to a factor (1 ± ε), provided that m = Ω(ε^{-2} lg n). The transform has fo…
View article: On the Hierarchy of Distributed Majority Protocols
On the Hierarchy of Distributed Majority Protocols Open
We study the consensus problem among n agents, defined as follows. Initially, each agent holds one of two possible opinions. The goal is to reach a consensus configuration in which every agent shares the same opinion. To this end, agents r…
View article: Dynamic Averaging Load Balancing on Arbitrary Graphs
Dynamic Averaging Load Balancing on Arbitrary Graphs Open
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is ave…
View article: LIPIcs, Volume 254, STACS 2023, Complete Volume
LIPIcs, Volume 254, STACS 2023, Complete Volume Open
LIPIcs, Volume 254, STACS 2023, Complete Volume
View article: Distributed Averaging in Opinion Dynamics
Distributed Averaging in Opinion Dynamics Open
We consider two simple asynchronous opinion dynamics on arbitrary graphs where every node $u$ has an initial value $ξ_u(0)$. In the first process, the NodeModel, at each time step $t\ge 0$, a random node $u$ and a random sample of $k$ of i…
View article: Inference of a Rumor's Source in the Independent Cascade Model
Inference of a Rumor's Source in the Independent Cascade Model Open
We consider the so-called Independent Cascade Model for rumor spreading or epidemic processes popularized by Kempe et al.\ [2003]. In this model, a small subset of nodes from a network are the source of a rumor. In discrete time steps, eac…
View article: Asynchronous Opinion Dynamics in Social Networks
Asynchronous Opinion Dynamics in Social Networks Open
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation pr…
View article: Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem
Loosely-Stabilizing Phase Clocks and The Adaptive Majority Problem Open
We present a loosely-stabilizing phase clock for population protocols. In the population model we are given a system of n identical agents which interact in a sequence of randomly chosen pairs. Our phase clock is leaderless and it requires…
View article: Infinite Balanced Allocation via Finite Capacities
Infinite Balanced Allocation via Finite Capacities Open
We analyze the following infinite load balancing process, modeled as a classical balls-into-bins game: There are n bins (servers) with a limited capacity (buffer) of size c=c(n)∈N . Given a fixed arrival rate λ=λ(n)∈(0,1) , in every round …
View article: Self-Stabilizing Phase Clocks and the Adaptive Majority Problem.
Self-Stabilizing Phase Clocks and the Adaptive Majority Problem. Open
We present a self-stabilising phase clock for population protocols. In the population model we are given a system of $n$ identical agents which interact in a sequence of randomly chosen pairs. Our phase clock is leaderless and it requires …
View article: Fast Consensus via the Unconstrained Undecided State Dynamics
Fast Consensus via the Unconstrained Undecided State Dynamics Open
We consider the plurality consensus problem among $n$ agents. Initially, each agent has one of $k$ different opinions. Agents choose random interaction partners and revise their state according to a fixed transition function, depending on …
View article: Randomized renaming in shared memory systems
Randomized renaming in shared memory systems Open
View article: Die Schwierigkeiten bei der Modellierung von Epidemien
Die Schwierigkeiten bei der Modellierung von Epidemien Open
Damit sich Infektionen ausbreiten können, müssen Menschen miteinander in Kontakt stehen, also eine Art Netzwerk bilden. Bei Modellierungen solcher sozialen Netzwerke und auch in vielen anderen Anwendungen spielen sogenannte Graphen ein gro…
View article: Optimal time and space leader election in population protocols
Optimal time and space leader election in population protocols Open
Full verions, including all proofs
View article: Simulating Population Protocols in Sub-Constant Time per Interaction
Simulating Population Protocols in Sub-Constant Time per Interaction Open
We consider the efficient simulation of population protocols. In the population model, we are given a system of n agents modeled as identical finite-state machines. In each step, two agents are selected uniformly at random to interact by u…
View article: Simulating Population Protocols in Sub-Constant Time per Interaction
Simulating Population Protocols in Sub-Constant Time per Interaction Open
We consider the efficient simulation of population protocols. In the population model, we are given a system of n agents modeled as identical finite-state machines. In each step, two agents are selected uniformly at random to interact by u…
View article: On Counting the Population Size
On Counting the Population Size Open
We consider the problem of counting the population size in the population model. In this model, we are given a distributed system of $n$ identical agents which interact in pairs with the goal to solve a common task. In each time step, the …
View article: Tight & Simple Load Balancing
Tight & Simple Load Balancing Open
We consider the following load balancing process for m tokens distributed arbitrarily among n nodes connected by a complete graph. In each time step a pair of nodes is selected uniformly at random. Let ℓ 1 and ℓ 2 be their respective numbe…
View article: Improved Analysis of Deterministic Load-Balancing Schemes
Improved Analysis of Deterministic Load-Balancing Schemes Open
We consider the problem of deterministic load balancing of tokens in the discrete model. A set of n processors is connected into a d -regular undirected network. In every timestep, each processor exchanges some of its tokens with each of i…
View article: A population protocol for exact majority with $O(\\log^{5/3} n)$ stabilization time and asymptotically optimal number of states.
A population protocol for exact majority with $O(\\log^{5/3} n)$ stabilization time and asymptotically optimal number of states. Open
A population protocol is a sequence of pairwise interactions of n agents. During one interaction, two randomly selected agents update their states by applying a deterministic transition function. The goal is to stabilize the system at a de…
View article: Simple Load Balancing
Simple Load Balancing Open
We consider the following load balancing process for $m$ tokens distributed arbitrarily among $n$ nodes connected by a complete graph: In each time step a pair of nodes is selected uniformly at random. Let $\ell_1$ and $\ell_2$ be their re…