arXiv subjects

Stefan Schmid

Publications and source records attributed to Stefan Schmid.

At least 19 recordsLinked to original sources

arXiv2026

Fast Multidimensional Approximate Agreement with Optimal Resilience Using Ball Validity

Multidimensional approximate agreement requires $n$ processes with inputs in $\mathbb{R}^d$ to output vectors close to each other, despite up to $t$ Byzantine faults. Under convex validity, outputs must lie in the convex hull of the correct inputs, which leads to resilience thresholds that grow with the dimension. We instead study Minimum Enclosing Ball (MEB) validity and its multiplicative relaxation $c$-MEB validity. Our first contribution is Adaptive MEB Contraction, a coordinate-free algorithm that, in the synchronous model with $n>(d+1)t$ contracts the correct MEB radius by $1/\sqrt2$ per round for $α=1$ while satisfying $\sqrt2$-MEB validity. We also give an example showing that this bound is tight for our analysis. Our main technical contribution is a dimension-free inflation theorem: if every $β$ balls in a finite family of Euclidean balls have a common point, then inflating each radius by $\sqrt{β/(β-1)}$ guarantees a common intersection. Applying the theorem to the candidate balls defining the local MEB-safe areas results in a synchronous algorithm with optimal resilience $n>3t$, contraction factor $\sqrt3/2$ and $\sqrt6$-MEB validity. To the best of our knowledge, this is the first multidimensional approximate agreement algorithm with optimal resilience, constant $c$-MEB validity and coordinate-free contraction. We further extend the approach to the asynchronous setting. Without inflation we obtain resilience $n>(d+2)t$, contraction factor $\sqrt{2/3}$ and $\sqrt6$-MEB validity, whereas with inflation for $n>4t$ we get the contraction factor $\sqrt{15}/4$ and $2\sqrt{10}$-MEB validity. Finally, we compare our guarantees with existing algorithms, including Minimum-Diameter Averaging (MDA), for which we derive MEB-validity guarantees. Our algorithms achieve strictly better resilience while providing substantially stronger MEB-validity guarantees than MDA.

cs.DC↗

arXiv2026

Revisiting Bruck: Phase-Efficient All-to-All Collective Communication in Reconfigurable Networks

All-to-All collective communication is a key performance bottleneck for distributed machine learning (ML) and high-performance computing (HPC) workloads, where dense traffic increasingly stresses scale-up interconnects. While these ML and HPC workloads have driven unprecedented infrastructure demand, optical reconfigurable networks (ORNs) offer a promising path forward as they can reconfigure the network at runtime. By adapting the physical topology to the active workload, they improve communication cost and bandwidth utilization. However, optical reconfigurable networks introduce a fundamental trade-off for collective communication: each reconfiguration requires global synchronization, during which communication is suspended for at a non-negligible delay. Additionally, their benefit is critically contingent on whether the collective consists of structured phases that can be served by sparse and reusable topology states. In this paper, we revisit Bruck's All-to-All implementation and demonstrate the benefits of topology optimization in which both communication pattern and reconfiguration strategy are co-designed. We present ReTri, a bidirectional All-to-All schedule for ORNs based on the Trivance algorithm. ReTri uses balanced ternary block propagation to complete All-to-All in $\lceil \log_3 n\rceil$ phases. The reconfiguration strategy induced by ReTri's pairwise bidirectional exchanges allows reconfiguration delays to be amortized across multiple phases. Preliminary simulations show that ReTri improves completion time by up to $10\times$ over Pairwise All-to-All, even for millisecond-scale reconfiguration delays, and improves reconfigurable Bruck by up to $2.1\times$.

cs.DC↗

arXiv2026

An Improved Subquadratic Bound for Online Bisection

The online bisection problem is a natural dynamic variant of the classic bisection problem, where one has to dynamically maintain a partition of $n$ elements into two clusters of cardinality $n/2$. During runtime, an online algorithm is given a sequence of requests, each being a pair of elements: an~inter-cluster request costs one unit while an intra-cluster one is free. The algorithm may change the partition, paying a unit cost for each element that changes its cluster. This natural problem admits a simple deterministic $O(n^2)$-competitive algorithm [Avin et al., DISC 2016]. While several significant improvements over this result have been obtained since the original work, all of them either limit the generality of the input or assume some form of resource augmentation (e.g., larger clusters). Moreover, the algorithm of Avin et al. achieves the best known competitive ratio even if randomization is allowed. In this paper, we present the first randomized online algorithm that breaks this natural quadratic barrier and achieves a competitive ratio of $\tilde{O}(n^{11/6})$ without resource augmentation and for an arbitrary sequence of requests.

cs.DS↗

arXiv2026

Designing Caterpillars for Graphs: Approximation and Hardness

The classical Minimum Linear Arrangement (MLA) problem has been studied extensively. It is known to be NP-hard and it admits an $O(\sqrt{\log n}\log\log n)$-approximation [Feige and Lee, IPL, 2007]. MLA can be defined as follows as design problem: Given a graph $G$ with vertex set $V(G)$, design a path $H$ on the same vertex set that minimizes the linear arrangement cost $\sum_{uv\in E(G)}\textrm{dist}_H(u,v)$, where $\textrm{dist}_H(u,v)$ indicates the distance of $u$ and $v$ in $H$. We initiate the study of the generalization in which $H$ is allowed to be a caterpillar graph of maximum degree at most $Δ$. Caterpillars are the simplest generalization of paths, having pathwidth one and interpolating between paths and stars via the degree parameter $Δ$. We give an algorithm that lifts any $α$-approximation for MLA to an $(α+3-2/(Δ-1))$-approximation for our problem, thus obtaining an $O(\sqrt{\log n}\log\log n)$-approximation for our more general problem as well. Moreover, we derive a $4$-approximation whenever MLA is polynomial-time solvable, in particular, for trees. Complementing these results, we prove NP-hardness for every constant $Δ\geq 2$, and, in stark contrast to MLA, show it remains NP-hard on trees when $Δ$ is part of the input.

cs.DS↗

arXiv2026

Liquid democracy under vote correlation: On the fallacies of averaging and the excluded middle

Liquid democracy permits voters to vote directly or delegate their votes to others. Existing algorithmic analyses assign each voter a single scalar parameter, interpreted as an independent probability of voting for the ground truth. This representation is inadequate when delegation is fixed before public information changes different voters' reliability in different ways. In this work, we study a minimal common-signal model of this phenomenon. Delegation occurs before a public binary signal is realised, while voting occurs afterwards. Conditional on the signal, sink votes are independent, and each voter has a signal-specific competence; marginally, correctness events are correlated through the common signal. We show that delegation based on average competence is not a safe scalarisation: it can violate do-no-harm, and a beneficial delegation rule may send votes to voters with lower average competence. We present and analyse three novel delegation mechanisms for this setting. The first is a conservative intersection mechanism that delegates only to neighbours whose competence exceeds the delegator's by a prescribed margin in every signal state; the conservative intersection mechanism inherits all the guarantees of delegation in the scalar competence setting. The next mechanism is a confounded-set mechanism that enable the delegation to neighbours who are favoured in one state and worse by at most a prescribed tolerance in the other. For this mechanism, we prove expected-margin bounds, and identify the weight-dispersion and mechanism-concentration conditions needed to obtain majority-correctness guarantees. Finally, on bounded-in-degree graphs, a multi-round certified-path mechanism propagates nonnegative two-dimensional path certificates; it is acyclic, yields statewise terminal competence improvement, and gives uniform bounds on path length and terminal voting weight.

cs.GT↗

arXiv2026

OntoExtend: A Framework for Requirement-driven and Scalable Ontology Extension with LLMs

Ontology extension refers to the process of enriching an existing ontology in response to emerging requirements, making it more complete. This task is a resource-intensive and error-prone process. Large Language Models (LLMs) have shown promising performance on generating ontologies from scratch, but current approaches rarely tie ontology extension explicitly to requirements or reusable core models, and offer limited, systematic evaluation of LLM outputs. This paper introduces OntoExtend, a requirements-driven framework for ontology extension with LLMs. It uses retrieval-augmented generation (RAG) over relevant input ontologies and requirements in the form of competency questions to propose grounded extensions. We evaluate OntoExtend on 39 CQs from two use cases: a public EU-project ontology, Onto-DESIDE, and an industrial ontology from Bosch. The generated fragments show few structural issues, satisfy all functional evaluation tests, and are rated by ontology engineers as requiring minor to moderate revision before integration. These results suggest that OntoExtend is useful as a drafting assistant for requirement-driven ontology extension in real world scenarios, while remaining sensitive to CQ specificity and modelling profile.

cs.AI↗

arXiv2026

Privacy Attacks on Stable Marriage

The stable marriage problem appears in many privacy-sensitive domains, for example in the National Resident Matching Program in the US. In such applications, preserving the privacy of users' preference lists is essential to prevent strategic manipulation, discourage misreporting, and comply with data protection regulations. In this work, we investigate privacy attacks on stable marriage algorithms. Assuming that the attacker (e.g., the hospitals) can repeatedly interact with the stable marriage algorithm, we demonstrate how such interactions can reveal private preferences of the non-malicious side (e.g., the residents). We show that the widely applied Gale-Shapley Matching Algorithm, where the proposers' side is malicious, is vulnerable to privacy attacks and all honest agents' preferences can be revealed. We further investigate which preference distributions of the honest, non-malicious side are susceptible to privacy attacks and show that the Gale-Shapley Matching Algorithm where the honest side proposes can preserve privacy in non-susceptible preference distributions. We extend our results to the decentralized setting and show that the attacker's side can infer all preference orderings. In an experimental evaluation, we test privacy attacks on synthetic and real-world data and show that real-world data is indeed susceptible to privacy attacks. This work underlines a need for new privacy-preserving stable marriage algorithms.

cs.DS↗

arXiv2026

Trivance: Latency-Optimal AllReduce by Shortcutting Multiport Networks

AllReduce is a fundamental collective communication operation in distributed computing and a key performance bottleneck for large-scale training and inference. Its completion time is determined by the number of communication steps, which dominate latency-sensitive workloads, and the communication distance affecting both latency- and bandwidth-bound regimes. Direct-connect topologies, such as Google's TPUv4 tori, are particularly prone to large communication distances due to limited bisection bandwidth. In this paper, we present Trivance, a novel AllReduce algorithm that completes within $\log_3 n$ steps - a 50% improvement in comparison to Swing and Recursive Doubling, while reducing congestion compared to Bruck's algorithm by a factor of three and preserving bandwidth-optimality. Trivance exploits both transmission ports of a bidirectional ring within each step to triple the communication distance along both directions simultaneously. By performing joint reductions, Trivance improves both the number of steps and network congestion. We further show that Trivance extends naturally to multidimensional torus networks, retaining its latency advantage while achieving performance comparable to bandwidth-optimal algorithms for large AllReduce sizes. Our packet-level SST simulation shows that Trivance improves state-of-the-art approaches by 5-30% for AllReduce sizes up to 8 MiB, in high-bandwidth settings up to 32 MiB and for 3D tori up to 128 MiB. Throughout the evaluation, Trivance remains the best-performing latency-optimal algorithm.

cs.DC↗

arXiv2026

Rethinking Fronthaul Topologies for Cell-Free 6G Networks

Due to significant progress in physical layer (PHY) technologies, future 6G networks are expected to feature much denser antenna deployments. Cell-free MIMO network designs are one of the most promising candidates to enable denser networks. While significant effort has been put into its PHY research, the challenges it brings to networking disciplines remain relatively unexplored. In this work, we propose various fronthaul network designs for cell-free MIMO. Our results show that while tree topologies may suffice for small-scale deployments, they become infeasible as the number of antennas increases. In contrast, with growing network size, the proposed Clos topology performs almost as well as the optimal topology.

cs.IT↗

arXiv2026

SecureClaw: Clawing Back Control of LLM Agents

Tool-using large language model (LLM) agents face two distinct security failures: unauthorized external actions and exposure of sensitive plaintext inside the runtime before any final output check can intervene. Existing defenses usually protect one boundary, either the planner/runtime or the action sink, and therefore do not by themselves secure both surfaces. We present SecureClaw, a dual-boundary architecture that places authorization at the effect sink and plaintext confinement at the read boundary. Sensitive reads pass through a trusted gateway that replaces raw values with opaque handles and, in the evaluated deployment, bounded summaries as an explicit declassification interface. Writes that change external state follow a PREVIEW$\rightarrow$COMMIT protocol in which only a trusted executor may commit the exact canonical request authorized by policy. The runtime can still plan over summaries and symbolic references, but cannot directly dereference secrets or perform side effects. Across AgentDojo, AgentLeak, and Agent Security Bench (ASB), SecureClaw is the only defense we evaluate in a common harness that simultaneously retains usable task utility and achieves 0\% attack success rate (ASR) on ASB, 0.64\% ASR on AgentDojo, and 3.23\% overall leak on AgentLeak's attacked parity lane, which measures final-output and internal-relay leakage.

cs.CR↗

arXiv2026

FuseFSS: Efficient Secure LLM Inference with Function Secret Sharing

Two-server secure inference allows a client to query a hosted large language model (LLM) without revealing prompts or embeddings. Recent GPU systems based on function secret sharing (FSS) make linear layers efficient, but fixed-point nonlinearities and helper operations remain a bottleneck because each operator is typically implemented as a bespoke protocol with its own comparisons, wrap-around corrections, and preprocessing material. We present FuseFSS, a compiler that replaces per-operator protocol design with a single compilation pipeline. For each scalar fixed-point operator, a compact specification lists its interval partition, low-degree arithmetic pieces, and required predicate bits. The compiler emits two batched FSS evaluations on the public masked value: one packed comparison that returns all predicate bits, and one vector interval lookup that returns the active coefficients and constants. Compared to the current state-of-the-art FSS-based GPU secure inference, FuseFSS preserves accuracy while achieving a $1.24\times$--$1.50\times$ end-to-end speedup and reducing online communication by $9\%$--$16\%$ on BERT and GPT-style models; preprocessing is also lighter, with $14\%$--$23\%$ lower key-generation time and $20\%$--$24\%$ smaller keys.

cs.CR↗

arXiv2026

Resilient Byzantine Agreement with Predictions

This paper studies the Byzantine Agreement problem where the nodes have access to a predictor that flags nodes for suspicion of faulty (Byzantine) behavior. We focus on algorithmic resilience -- the maximum number of faulty nodes an algorithm can tolerate -- and present algorithms and impossibility results whose resilience depend on the accuracy of the predictor. As our first main result, we bring a complete characterization of the consistency--robustness trade-offs in both the non-authenticated and authenticated settings: for $n$ nodes and a parameter $α\in [0, 1]$, we present algorithms that tolerate up to $α\cdot n$ faulty nodes when the predictor is correct (consistency), and up to $\frac{1-α}{2} \cdot n - 1$ faulty nodes when the predictor is arbitrarily wrong (robustness); in the authenticated setting the robustness bound improves to $(1-α) \cdot n - 1$. These trade-offs are exactly tight as we show that one additional faulty node renders the problem impossible. Our second main result characterizes smoothness: the rate at which resilience degrades as the predictor becomes less accurate. We show that resilience linearly decreases in the number of wrong predictions as long as that number stays within a constant fraction of $n$. Concretely, in the non-authenticated setting each additional wrong prediction loses one unit of resilience, whereas in the authenticated setting the decline is halved since two wrong predictions are needed to lose one unit of resilience.

cs.DC↗

arXiv2026

Ranking Opinions with Few States in Population Protocols

Population protocols are a model of distributed computing where $n$ agents, each a simple finite-state machine, interact in pairs to solve a common task against a (adversarial) interaction scheduler. This model was intensively studied in recent years; in particular, the problem of relative majority received much attention: Each agent starts with an input opinion (or color) out of $k$ possibilities, and the goal is for each agent to eventually output the color with the largest support in the population. Before our work, the state complexity (the minimum number of states required per agent) was only known to be between $Ω(k^2)$ and $O(k^{7})$. Our main contribution is a population protocol that solves the relative majority problem with $k^3$ states. We achieve this result with a new protocol called CIRCLES. While prior approaches in the literature relied on duels of agents to find the majority color -- an approach that proved effective for the case with two colors -- CIRCLES partitions the agents into circular linked lists of decreasing sizes, with the property that no two agents with the same initial color lie in the same circle. We show that CIRCLES always correctly computes the desired structure against the most adversarial of schedulers (weakly fair). We then show that a trivial extension of CIRCLES solves the relative majority problem. We extend our protocol to handle various tie-breaking mechanisms or to support the case where the agents do not share a prior ordering of the colors. Finally, we show that a modification of CIRCLES solves the ranking problem with $2 \cdot k^4$ states, where each agent must output the rank of its initial color in the population.

cs.DC↗

arXiv2026

Competitive Transaction Admission in PCNs: Online Knapsack with Positive and Negative Items

Payment channel networks (PCNs) are a promising approach to making cryptocurrency transactions faster and more scalable. At their core, PCNs bypass the blockchain by routing transactions through intermediary channels. However, a channel can forward a transaction only if it has the necessary funds: the problem of keeping the channels balanced is a current bottleneck for the PCN's transaction throughput. This paper considers the problem of maximizing the number of transactions accepted by a channel in a PCN. Previous works either considered the associated optimization problem with all transactions known in advance or developed heuristics tested on particular transaction datasets. This work, however, considers the problem in its purely online form where the transactions are arbitrary and revealed one after the other. We show that the problem can be modeled as a new online knapsack variant where the items (transaction proposals) can be either positive or negative depending on the direction of the transaction. The main contribution of this paper is a deterministic online algorithm that is $O(\log B)$-competitive, where $B$ is the knapsack capacity (maximum allowed channel balance). We complement this result with an asymptotically matching lower bound of $Ω(\log B)$ which holds for any randomized algorithm, demonstrating our algorithm's optimality.

cs.DS↗

arXiv2026

Online Algorithms with Unreliable Guidance

This paper introduces online algorithms with unreliable guidance (OAG), a model for ML-augmented online decision-making that cleanly separates the predictive and algorithmic components, thus offering a single, well-defined analysis framework that depends only on the problem at hand. Formulated through the lens of request-answer games, the OAG model brings multiple concepts (predictions from the answer space, guide, anytime competitiveness) which enable learning-augmented algorithms to be analyzed independently of predictor-specific choices - such as prediction semantics, error functions, or probing strategies - that would otherwise restrict the algorithm's generality and applicability. The clean framework of the OAG model allows to build the first generic compiler, the drop-or-trust-blindly (DTB) compiler, that turns almost any standard, prediction-free online algorithm into a learning-augmented one. Although simple, we show that the DTB compiler produces new learning-augmented algorithms with strong consistency-robustness guarantees for three classic online problems: we achieve new trade-offs for bipartite matching with adversarial arrival order, and obtain optimal solutions for caching and uniform metrical task systems.

cs.AI↗

arXiv2026

Online Graph Embedding in Star Graphs

Graph embedding is a fundamental problem of mapping nodes of a guest graph into a host graph while minimizing the distance distortion, with broad applications, including virtual network embeddings into physical topologies, VLSI design, or community detection in social networks. However, in many real-world applications the guest graph changes over time and the embedding can adapt to these changes (e.g. virtual machine migration in network embeddings). Static embeddings are inherently inefficient in comparison to adaptive embeddings, but it remains an unresolved algorithmic challenge to design efficient embedding algorithms that adapt to the demand on-the-fly, i.e., that are online. In this paper, we derive optimal deterministic and randomized online algorithms for the online graph embedding problem in star host graphs. This is an essential building block on the way to design algorithms for more complex host graphs, representing a single node and its neighborhood. We start by presenting a $1.5$-competitive deterministic algorithm and showing that no deterministic algorithm can perform better. Our main contribution is a randomized algorithm that achieves a significantly better competitive ratio of $11/9 \approx 1.222$. Both the deterministic and the randomized algorithms are optimal, which we prove by deriving tight lower bounds for the competitiveness of any algorithm.

cs.DS↗

arXiv2026

Practical Validity Conditions for Byzantine-Tolerant Federated Learning

Robust aggregation is the core operation in Byzantine-tolerant federated learning. To ensure the quality of aggregation independently of data distribution or attacks, validity conditions are needed. They provide geometric guarantees of where the output of the aggregation must lie. The widespread convex validity requires the output to lie in the convex hull of the honest vectors. Although this guarantee is strong in theory, it is poorly suited to modern federated learning systems, as it has dimension-dependent resilience and excludes many practical aggregation rules. We introduce the minimum enclosing ball (MEB) validity condition for robust aggregation, as well as its multiplicative relaxation, $c$-MEB validity, where $c$ is a constant. We show that exact MEB validity still suffers from limited resilience, while relaxed $c$-MEB validity is achievable if a majority of clients is honest, i.e. $n>2t$. We give an optimal MinMax-MEB rule for the relaxed condition with the bound $c<\sqrt{2}$ and prove explicit relaxed-MEB guarantees for standard aggregators including minimum-diameter averaging, medoid and geometric median. Finally, we relate MEB validity to convex, relaxed-convex and box validity studied in prior literature, thus providing a systematic map of geometric validity conditions for Byzantine-robust aggregation. Our results show that relaxed MEB validity connects validity conditions in distributed computing and Byzantine-tolerant aggregation rules, and offers a practical alternative to convex validity.

cs.LG↗

arXiv2026

Bridge: Optimizing Collective Communication Schedules in Reconfigurable Networks with Reusable Subrings

Optical circuit-switched networks have emerged as an appealing alternative to electrical fabrics as they can reconfigure the network topology at runtime, reducing communication cost and improving bandwidth utilization. Yet exploiting optical reconfigurable networks for collective communication comes with a fundamental trade-off: each reconfiguration incurs non-negligible delay, communication must pause while the fabric reconfigures, and the benefit of a new topology depends on future traffic. The central question is therefore when reconfiguration is worth its cost. While prior work has demonstrated the benefits of reconfiguration, existing strategies use optical links only to optimize the current step, without reusing them for future steps. In this paper, we present Bridge, a reconfiguration strategy for important collective communication primitives used in AI/ML and HPC applications, namely All-to-All, AllReduce, Reduce-Scatter, and AllGather. Bridge exploits the structure of Bruck's communication pattern to support efficient sparse reconfiguration. The key idea is to reduce propagation and transmission delay by directly connecting immediate communication partners and preserve efficient reachability to future peers through connected subrings. As a result, optical links can be reused across multiple subsequent steps, allowing the benefit of reconfiguration to amortize beyond a single step. Our evaluation shows that Bridge reduces All-to-All completion time by typically $3\times$ to $10\times$ over static baselines even with millisecond-scale reconfiguration delays. For AllReduce, Bridge uniformly outperforms existing reconfiguration strategies, delivers up to $1.5\times$ speedup, and exceeds the bandwidth-optimal Ring algorithm by $1.5\times$ to $6.6\times$ on low to moderate-sized workloads.

cs.NI↗