arXiv subjects

Dominik Kaaser

Publications and source records attributed to Dominik Kaaser.

At least 19 recordsLinked to original sources

arXiv2026

Counting in Population Protocols on Graphs

We consider the problem of counting the number of agents in a population protocol where the agents are connected by an underlying graph $G=(V,E)$ with $|V|=n$ nodes. In each step, a random scheduler selects an edge uniformly at random, and the incident nodes make a state transition. As per standard assumptions, agents are identical and anonymous, that is, have no identifiers. To break symmetry, in each interaction one of the agents is declared as the initiator uniformly at random. Our size counting protocol uses $\tilde O(n)$ states and stabilizes in $O( B(G) \cdot \log^2(n) + L(G) \cdot \log(n))$ interactions with high probability, where $B(G)$ is the broadcast time and $L(G)$ is the load balancing time. Our protocol is based on novel protocols for sampling independent random bits (given that the scheduler determines an initiator and responder) and approximating $\log n$ up to an additive error of $O(\log \log n)$ with high probability. The latter uses $O(poly\log(n))$ states and $O(B(G)\cdot\log^2 n)$ interactions. Both results may be of independent interest. The main protocol for exact counting requires the presence of a unique leader, the other two do not. None of the protocols requires any knowledge about the graph $G$. We conclude with impossibility results for terminating uniform population protocols that compute graph-size properties (like counting nodes or determining parity) with and without a leader.

cs.DC↗

arXiv2026

Finding Patient Zero via Low-Dimensional Geometric Embeddings

We study the patient zero problem in epidemic spreading processes in the independent cascade model and propose a geometric approach for source reconstruction. Using Johnson-Lindenstrauss projections, we embed the contact network into a low-dimensional Euclidean space and estimate the infection source as the node closest to the center of gravity of infected nodes. Simulations on Erd\H{o}s-R\'enyi graphs demonstrate that our estimator achieves meaningful reconstruction accuracy despite operating on compressed observations.

cs.CG↗

arXiv2026

Fluctuations of the Ising free energy on Erd\H{o}s-R\'enyi graphs

We investigate the ferromagnetic Ising model on the Erd\H{o}s-R\'enyi random graph $\mathbb{G}(n,m)$ with bounded average degree $d=2m/n$. Specifically, we determine the limiting distribution of $\log Z_{\mathbb{G}(n,m)}(\beta,B)$, where $Z_{\mathbb{G}(n,m)}(\beta,B)$ is the partition function at inverse temperature $\beta>0$ and external field $B\geq0$. If either $B>0$, or $B=0$, $d>1$ and $\beta>\operatorname{ath}(1/d)$ the limiting distribution is a Gaussian whose variance is of order $\Theta(n)$ and is described by a family of stochastic fixed point problems that encode the root magnetisation of two correlated Galton-Watson trees. By contrast, if $B=0$ and either $d\leq1$ or $\beta<\operatorname{ath}(1/d)$ the limiting distribution is an infinite sum of independent random variables and has bounded variance.

math.CO↗

arXiv2025

(Almost) Perfect Discrete Iterative Load Balancing

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 each node has approximately the same number of tokens. We present results for a general class of simple local balancing schemes where the tokens are balanced via matchings. In each round the process averages the tokens of any two matched nodes. If the sum of their tokens is odd, the node to receive the one excess token is selected at random. Our class covers three popular models: in the matching model a new matching is generated randomly in each round, in the balancing circuit model a fixed sequence of matchings is applied periodically, and in the asynchronous model the load is balanced over a randomly chosen edge. We measure the quality of a load vector by its discrepancy, defined as the difference between the maximum and minimum load across all nodes. As our main result we show that with high probability our discrete balancing scheme reaches a discrepancy of $3$ in a number of rounds which asymptotically matches the spectral bound for continuous load balancing with fractional load. This result improves and tightens a long line of previous works, by not only achieving a small constant discrepancy (instead of a non-explicit, large constant) but also holding for arbitrary instead of regular graphs. The result also demonstrates that in the general model we consider, discrete load balancing is no harder than continuous load balancing.

cs.DC↗

arXiv2025

Silent Self-Stabilizing Ranking: Time Optimal and Space Efficient

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 assign each agent a unique rank in $\{1, \dots, n\}$. Given unique ranks, it is straightforward to select a designated leader. Thus, our protocol is a self-stabilizing leader election protocol as well. Ranking requires at least $n$ states per agent; hence, the goal is to minimize the additional number of states, called overhead states. The core of our protocol is a space-efficient but non-self-stabilizing ranking protocol that requires only $n + O(\log n)$ states. Our protocol stabilizes in $O(n^2\log n)$ interactions w.h.p.\ and in expectation, using $n + O(\log^2 n)$ states in total. Our stabilization time is asymptotically optimal (see Burman et al., PODC'21). In comparison to the currently best known ranking protocol by Burman et al., which requires $n + \Omega(n)$ states, our result exponentially improves the number of overhead states.

cs.DC↗

arXiv2024

SoK: Towards Security and Safety of Edge AI

Advanced AI applications have become increasingly available to a broad audience, e.g., as centrally managed large language models (LLMs). Such centralization is both a risk and a performance bottleneck - Edge AI promises to be a solution to these problems. However, its decentralized approach raises additional challenges regarding security and safety. In this paper, we argue that both of these aspects are critical for Edge AI, and even more so, their integration. Concretely, we survey security and safety threats, summarize existing countermeasures, and collect open challenges as a call for more research in this area.

cs.CR↗

arXiv2024

Dynamic Size Counting in the Population Protocol Model

The population protocol model describes collections of distributed agents that interact in pairs to solve a common task. We consider a dynamic variant of this prominent model, where we assume that an adversary may change the population size at an arbitrary point in time. In this model we tackle the problem of counting the population size: in the dynamic size counting problem the goal is to design an algorithm that computes an approximation of $\log n$. This estimate can be used to turn static, non-uniform population protocols, i.e., protocols that depend on the population size $n$, into dynamic and loosely-stabilizing protocols. Our contributions in this paper are three-fold. Starting from an arbitrary initial configuration, we first prove that the agents converge quickly to a valid configuration where each agent has a constant-factor approximation of $\log n$, and once the agents reach such a valid configuration, they stay in it for a polynomial number of time steps. Second, we show how to use our protocol to define a uniform and loosely-stabilizing phase clock for the population protocol model. Finally, we support our theoretical findings by empirical simulations that show that our protocols work well in practice.

cs.DC↗

arXiv2024

Population Protocols for Exact Plurality Consensus -- How a small chance of failure helps to eliminate insignificant opinions

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 opinion}) via random, pairwise interactions. The case of $k = 2$ opinions is known as the \emph{majority problem}. Recent breakthroughs led to an always correct, exact majority population protocol that is both time- and space-optimal, needing $O(\log n)$ states per agent and, with high probability, $O(\log n)$ time~[Doty, Eftekhari, Gasieniec, Severson, Stachowiak, and Uznanski; 2021]. We know that any always correct protocol requires $\Omega(k^2)$ states, while the currently best protocol needs $O(k^{11})$ states~[Natale and Ramezani; 2019]. For ordered opinions, this can be improved to $O(k^6)$~[Gasieniec, Hamilton, Martin, Spirakis, and Stachowiak; 2016]. We design protocols for plurality consensus that beat the quadratic lower bound by allowing a negligible failure probability. While our protocols might fail, they identify the plurality opinion with high probability even if the bias is $1$. Our first protocol achieves this via $k-1$ tournaments in time $O(k \cdot \log n)$ using $O(k + \log n)$ states. While it assumes an ordering on the opinions, we remove this restriction in our second protocol, at the cost of a slightly increased time $O(k \cdot \log n + \log^2 n)$. By efficiently pruning insignificant opinions, our final protocol reduces the number of tournaments at the cost of a slightly increased state complexity $O(k \cdot \log\log n + \log n)$. This improves the time to $O(n / x_{\max} \cdot \log n + \log^2 n)$, where $x_{\max}$ is the initial size of the plurality. Note that $n/x_{\max}$ is at most $k$ and can be much smaller (e.g., in case of a large bias or if there are many small opinions).

cs.DC↗

arXiv2024

Noisy group testing via spatial coupling

We study the problem of identifying a small set $k\sim n^\theta$, $0<\theta<1$, of infected individuals within a large population of size $n$ by testing groups of individuals simultaneously. All tests are conducted concurrently. The goal is to minimise the total number of tests required. In this paper we make the (realistic) assumption that tests are noisy, i.e.\ that a group that contains an infected individual may return a negative test result or one that does not contain an infected individual may return a positive test results with a certain probability. The noise need not be symmetric. We develop an algorithm called SPARC that correctly identifies the set of infected individuals up to $o(k)$ errors with high probability with the asymptotically minimum number of tests. Additionally, we develop an algorithm called SPEX that exactly identifies the set of infected individuals w.h.p. with a number of tests that matches the information-theoretic lower bound for the constant column design, a powerful and well-studied test design.

cs.DM↗

arXiv2023

Efficient Approximate Recovery from Pooled Data Using Doubly Regular Pooling Schemes

In the pooled data problem we are given $n$ agents with hidden state bits, either $0$ or $1$. The hidden states are unknown and can be seen as the underlying ground truth $σ$. To uncover that ground truth, we are given a querying method that queries multiple agents at a time. Each query reports the sum of the states of the queried agents. Our goal is to learn the hidden state bits using as few queries as possible. So far, most literature deals with exact reconstruction of all hidden state bits. We study a more relaxed variant in which we allow a small fraction of agents to be classified incorrectly. This becomes particularly relevant in the noisy variant of the pooled data problem where the queries' results are subject to random noise. In this setting, we provide a doubly regular test design that assigns agents to queries. For this design we analyze an approximate reconstruction algorithm that estimates the hidden bits in a greedy fashion. We give a rigorous analysis of the algorithm's performance, its error probability, and its approximation quality. As a main technical novelty, our analysis is uniform in the degree of noise and the sparsity of $σ$. Finally, simulations back up our theoretical findings and provide strong empirical evidence that our algorithm works well for realistic sample sizes.

cs.LG↗

arXiv2023

Fast Convergence of $k$-Opinion Undecided State Dynamics in the Population Protocol Model

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. Proving that the process also quickly solves the consensus problem for $k>2$ opinions has remained open, despite analogous results for larger $k$ in the related parallel gossip model. In this paper we prove such convergence: under mild assumptions on $k$ and on the initial number of undecided agents we prove that the USD achieves plurality consensus within $O(k n \log n)$ interactions with high probability, regardless of the initial bias. Moreover, if there is an initial additive bias of at least $Ω(\sqrt{n} \log n)$ we prove that the initial plurality opinion wins with high probability, and if there is a multiplicative bias the convergence time is further improved. Note that this is the first result for $k > 2$ for the USD in the population protocol model. Furthermore, it is the first result for the unsynchronized variant of the USD with $k>2$ which does not need any initial bias.

cs.DC↗

arXiv2023

Dynamic Averaging Load Balancing on Arbitrary Graphs

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 averaged over the edges of that matching. We analyze the discrete case where load items are indivisible, moreover our results also carry over to the continuous case where load items can be split arbitrarily. For the choice of the matchings we consider three different models, random matchings of linear size, random matchings containing only single edges, and deterministic sequences of matchings covering the whole graph. We bound the discrepancy, which is defined as the difference between the maximum and the minimum load. Our results cover a broad range of graph classes and, to the best of our knowledge, our analysis is the first result for discrete and dynamic averaging load balancing processes. As our main technical contribution we develop a drift result that allows us to apply techniques based on the effective resistance in an electrical network to the setting of dynamic load balancing.

cs.DC↗

arXiv2022

Distributed Key Generation with Smart Contracts using zk-SNARKs

Distributed Key Generation (DKG) is an extensively researched topic as it is fundamental to threshold cryptosystems. Emerging technologies such as blockchains benefit massively from applying threshold cryptography in consensus protocols, randomness beacons, and threshold signatures. However, blockchains and smart contracts also enable further improvements of DKG protocols by providing a decentralized computation and communication platform. For that reason, we propose a DKG protocol that uses smart contracts to ensure the correct execution of the protocol, allow dynamic participation, and provide crypto-economic incentives to encourage honest behavior. The DKG protocol uses a dispute and key derivation mechanism based on Zero-Knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) to reduce the costs of applying smart contracts by moving the computations off-chain, where the smart contract only verifies the correctness of the computation.

cs.CR↗

arXiv2022

Inference of a Rumor's Source in the Independent Cascade Model

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, each informed node "infects" each of its uninformed neighbors with probability $p$. While many facets of this process are studied in the literature, less is known about the inference problem: given a number of infected nodes in a network, can we learn the source of the rumor? In the context of epidemiology this problem is often referred to as patient zero problem. It belongs to a broader class of problems where the goal is to infer parameters of the underlying spreading model, see, e.g., Lokhov [NeurIPS'16] or Mastakouri et al. [NeurIPS'20]. In this work we present a maximum likelihood estimator for the rumor's source, given a snapshot of the process in terms of a set of active nodes $X$ after $t$ steps. Our results show that, for cycle-free graphs, the likelihood estimator undergoes a non-trivial phase transition as a function $t$. We provide a rigorous analysis for two prominent classes of acyclic network, namely $d$-regular trees and Galton-Watson trees, and verify empirically that our heuristics work well in various general networks.

cs.SI↗

arXiv2022

On the Hierarchy of Distributed Majority Protocols

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 randomly sample other agents and update their opinion according to a simple update function depending on the sampled opinions. We consider two communication models: the gossip model and a variant of the population model. In the gossip model, agents are activated in parallel, synchronous rounds. In the population model, one agent is activated after the other in a sequence of discrete time steps. For both models we analyze the following natural family of majority processes called $j$-Majority: when activated, every agent samples $j$ other agents uniformly at random (with replacement) and adopts the majority opinion among the sample (breaking ties uniformly at random). As our main result we show a hierarchy among majority protocols: $(j+1)$-Majority (for $j > 1$) converges stochastically faster than $j$-Majority for any initial opinion configuration. In our analysis we use Strassen's Theorem to prove the existence of a coupling. This gives an affirmative answer for the case of two opinions to an open question asked by Berenbrink et al. [2017].

cs.DC↗

arXiv2022

Distributed Reconstruction of Noisy Pooled Data

In the pooled data problem we are given a set of $n$ agents, each of which holds a hidden state bit, either $0$ or $1$. A querying procedure returns for a query set the sum of the states of the queried agents. The goal is to reconstruct the states using as few queries as possible. In this paper we consider two noise models for the pooled data problem. In the noisy channel model, the result for each agent flips with a certain probability. In the noisy query model, each query result is subject to random Gaussian noise. Our results are twofold. First, we present and analyze for both error models a simple and efficient distributed algorithm that reconstructs the initial states in a greedy fashion. Our novel analysis pins down the range of error probabilities and distributions for which our algorithm reconstructs the exact initial states with high probability. Secondly, we present simulation results of our algorithm and compare its performance with approximate message passing (AMP) algorithms that are conjectured to be optimal in a number of related problems.

cs.IT↗

arXiv2022

On the Parallel Reconstruction from Pooled Data

In the pooled data problem the goal is to efficiently reconstruct a binary signal from additive measurements. Given a signal $σ\in \{ 0,1 \}^n$, we can query multiple entries at once and get the total number of non-zero entries in the query as a result. We assume that queries are time-consuming and therefore focus on the setting where all queries are executed in parallel. For the regime where the signal is sparse such that $ || σ||_1 = o(n)$ our results are twofold: First, we propose and analyze a simple and efficient greedy reconstruction algorithm. Secondly, we derive a sharp information-theoretic threshold for the minimum number of queries required to reconstruct $σ$ with high probability. Our first result matches the performance guarantees of much more involved constructions (Karimi et al. 2019). Our second result extends a result of Alaoui et al. (2014) and Scarlett & Cevher (2017) who studied the pooled data problem for dense signals. Finally, our theoretical findings are complemented with empirical simulations. Our data not only confirm the information-theoretic thresholds but also hint at the practical applicability of our pooling scheme and the simple greedy reconstruction algorithm.

cs.DM↗

arXiv2022

Asynchronous Opinion Dynamics in Social Networks

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 processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not \mbox{influence each other.} We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of $\mathcal{O}(n|E|^2 (\varepsilon/\delta)^2)$ on the expected number of opinion updates until convergence, where $|E|$ is the number of edges of the social network. For the complete social network we show a bound of $\mathcal{O}(n^3(n^2 + (\varepsilon/\delta)^2))$ that represents a major improvement over the previously best upper bound of $\mathcal{O}(n^9 (\varepsilon/\delta)^2)$. Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.

cs.DS↗