Dynamic networks are graphs in which edges are available only at specific time instants, modeling connections that change over time. The dynamic network creation game studies this setting as a strategic interaction where each vertex represents a player. Players can add or remove time-labeled edges in order to minimize their personal cost. This cost has two components: a construction cost, calculated as the number of time instants during which a player maintains edges multiplied by a constant $α$, and a communication cost, defined as the average distance to all other vertices in the network. Communication occurs through temporal paths, which are sequences of adjacent edges with strictly increasing time labels and no repeated vertices. We show for the shortest distance (minimizing the number of edges) that the price of anarchy can be proportional to the number of vertices, contrasting the constant price conjectured for static networks.

We study deterministic exploration by a single agent in T-interval-connected graphs, a standard model of dynamic networks in which, for every time window of length T, the intersection of the graphs within the window is connected. The agent does not know the window size T, nor the number of nodes n or edges m, and must visit all nodes of the graph. We consider two visibility models, KT_0 and KT_1, depending on whether the agent can observe the identifiers of neighboring nodes. We investigate two fundamental questions: the minimum window size that guarantees exploration, and the optimal exploration time under sufficiently large window size. For both models, we show that a window size T = Ω(m) is necessary. We also present deterministic algorithms whose required window size is O(ε(n,m)· m + n log^2 n), where ε(n,m) = ln n/1 + ln m - ln n. These bounds are tight for a wide range of m, in particular when m = n^1+Θ(1). The same algorithms also yield optimal or near-optimal exploration time: we prove lower bounds of Ω((m - n + 1)n) in the KT_0 model and Ω(m) in the KT_1 model, and show that our algorithms match these bounds up to a polylogarithmic factor, while being fully time-optimal when m = n^1+Θ(1). This yields tight bounds when parameterized solely by n: Θ(n^3) for KT_0 and Θ(n^2) for KT_1.

A reliable communication primitive guarantees the delivery, integrity, and authorship of messages exchanged between correct processes of a distributed system. We investigate the necessary and sufficient conditions for reliable communication in dynamic networks, where the network topology evolves over time despite the presence of a limited number of Byzantine faulty processes that may behave arbitrarily (i.e., in the globally bounded Byzantine failure model). We identify classes of dynamic networks where such conditions are satisfied, and extend our analysis to message losses, local computation with unbounded finite delay, and authenticated messages.

In gossip learning, a network of nodes trains a shared model collaboratively, without a central coordinator, by repeatedly exchanging parts of their local models. The state-of-the-art protocol, Partitioned Token Gossip Learning (PTGL) of Hegedüs et al., splits the weight matrix into S fixed partitions and disseminates them using a token-based fairness mechanism coupled with per-neighbor metadata exchange. We revisit partition scheduling by analogy with peer-to-peer live streaming, where model partitions act as video chunks and partition age acts as chunk scarcity. The analogy yields a design space of two-stage selection strategies (partition first, or neighbor first), from which we instantiate ten concrete protocols collectively called Stream Learning. Our main finding is that the simplest of these protocols, which transmits the locally least-trained partition to a uniformly random neighbor (Ri), matches PTGL on fault-free workloads while requiring neither token counters nor metadata exchange. Under an adversarial 30

The pattern formation (PTF) problem requires mobile robots to form a specified target pattern. Existing papers investigated the PTF problem and revealed the effect of obliviousness and synchronization on distributed coordination of mobile robots. However, the PTF problem allows translation, rotation, and scaling of the target pattern. In this paper, we introduce a novel pattern formation problem, called the hardwired pattern formation (HwPTF) problem that requires the robots to form a given target pattern in a specified size. Although two oblivious semi-synchronous robots cannot solve the HwPTF problem of multiplicity two (i.e., the rendezvous problem), we show that they can solve the HwPTF problem without multiplicity. We also show that two oblivious asynchronous robots equipped with lights can solve the HwPTF problem, while oblivious asynchronous robots cannot. We finally present a size-adjusting algorithm for more than four oblivious semi-synchronous robots, that yields a HwPTF algorithm when combined with some existing pattern formation algorithms.

In this paper, we address the problem of uniformly deploying mobile robots in complete bipartite graphs. Specifically, when n robots are positioned arbitrarily at distinct nodes in a complete bipartite graph K-n,K- n, which consists of two n-node sets V-L and V-R, the uniform deployment problem requires the robots to achieve one of the following configurations: (a) each node in V-L is occupied by exactly one robot, with no robots in V-R, or (b) each node in VR is occupied by exactly one robot, with no robots in V-L. In either configuration, the distance between any two robots is 2, ensuring that the robots are uniformly deployed. In this paper, we explore the relationship between the visibility range of robots and the solvability of the uniform deployment problem. First, we characterize solvable and unsolvable initial configurations under the assumption that robots have an infinite visibility range. Next, we demonstrate that visibility range 1 (meaning robots can only observe nodes at a distance of 1 and the robots positioned on them) is insufficient, proving the impossibility of solving the problem under this constraint. Conversely, we show that visibility range Theta(log n) is sufficient by presenting an algorithm that solves the uniform deployment problem in O(1) rounds, starting from any solvable initial configuration. Finally, we briefly introduce an example showing that robots with a constant visibility range (which is 3 in this example) cannot solve the problem in a native way.

We consider the problem of implementing Message-Adversary and Byzantine Tolerant Reliable Broadcast (MBRB) on top of an arbitrary topology network. The network consists of $n$ distinct nodes where $(i)$ up to $t$ nodes may behave arbitrarily (Byzantine faults), and (ii) a message adversary can drop up to $d$ messages for each local broadcast. We first investigate the solvability of the MBRB problem under different types of message adversaries, and we prove lower bounds for various validity conditions. We show these bounds are tight by demonstrating the existence of a simple protocol for solving the MBRB problem. We then validate these theoretical findings by implementing and testing BRB protocols under diverse network topologies using Quantas, a simulator dedicated to distributed algorithms. We analyze how performance metrics, including average delivery time, fraction of correct nodes delivering the message, and communication overhead, evolve as the adversarial power increases (i.e., by varying $t$ and $d)$.

Perfect Byzantine common coins, also known as strong coins, enable more efficient solutions to the consensus problem, and in general to Byzantine Fault-Tolerant State Machine Replication and blockchains, which is why multiple protocols opt to rely on them. On the other hand, perfect Byzantine common coins are costly to implement, which is why other protocols only rely on imperfect Byzantine common coins, also known as weak coins. This paper explores the impact of imperfect Byzantine common coins on the correctness of asynchronous consensus protocols that rely on a perfect common coin. To complement the well-studied probabilistic common coin, we introduce the concept of a t-Byzantine common coin. We then study the correctness of three well-known perfect common coin consensus protocols, highlighting the impact on their usage of the common coin, and attribute the results to the algorithmic structure of these protocols. In particular, we show that the FMR protocol[14] completely breaks under an imperfect common coin, both probabilistic and t-Byzantine. In contrast, the MMR [24] and CKS [8] protocols maintain safety under an imperfect common coin. Interestingly, MMR is live when using a probabilistic common coin, although the expected termination time might be prolonged. Yet, MMR is not live when using a t-Byzantine common coin. Finally, CKS loses its liveness under both variants of imperfect common coins. For the case of a t-Byzantine common coin, we show a simple fix for CKS when f+t<n/3.

We study the impact of restricting the class of separator problems on the look-compute-move mobile robot model hierarchy. In particular, we show that reachability specifications are sufficient to separate the semi-synchronous and the asynchronous model variants when robots agree on the unit-distance, but the two model variants are equivalent when considering terminating problems and no coordinate system agreement.

We consider the problem of gathering in finite time and at the same location, not known beforehand, a set of deterministic semi-synchronous robots, starting from an arbitrary initial configuration that may even be bivalent (that is, a configuration where the robots are evenly split on two different locations). This problem is known to be unsolvable when the robots are oblivious, that is, when they cannot remember their past actions. We present a deterministic gathering algorithm where robots may remember and communicate one bit of memory. This bit may be arbitrarily (and adversarially) set in the initial configuration. Our solution is thus memory optimal and self-stabilizing. Its proof of correctness is formally certified by the Coq proof assistant using the Pactole framework.

We consider the stronger version of the gathering problem for n autonomous mobile robots that evolve in a line graph: if there is no crash, the robots must gather as usual, and if there is a single crash location, the remaining correct robots have to gather at this location. The robots have very weak capabilities: their vision is limited and depends on the initial maximum distance between the robots, they are unaware of n, and they either retain no memory of the past, or retain a fixed number of states. In this context, we clarify the problem solvability according to visibility range and memory. If the initial number of occupied nodes is odd, we show that (i) an oblivious (that retains no past memory) algorithm can solve the problem if the visibility radius is one more hop than the trivial lower bound, and that bound is tight, and (ii) robots with one bit of persistent memory can solve the problem with optimal visibility radius, which is also tight with respect to the persistent memory. In the more relaxed setting where the initial number of occupied nodes may be even (but in that case, the distance between the border robots must be even), our one-bit memory algorithm remains valid (and optimal), while we present an oblivious algorithm for the same setting that uses two more hops than our lower bound.

Decentralized learning enhances privacy, scalability, and fault tolerance by distributing data and computation across nodes. A popular approach is Federated learning, which relies on a central aggregator, yet faces challenges such as server vulnerabilities, scalability issues, privacy risks and most importantly, the single point of failure. Alternatively Gossip Learning and Epidemic Learning offer fully decentralization through peer-to-peer exchanges of model updates, ensuring robustness and privacy, at the price of slower model convergence. In this work, we introduce a novel decentralized learning framework called HEAL. HEAL is the first cross-layer decentralized learning framework that exploits an optimized self-organizing and self-healing underlying P2P overlay combining the strengths of Federated Learning, Gossip and Epidemic Learning. Leveraging the recently proposed Elevator algorithm, HEAL promotes dynamically chosen nodes to act as aggregators. Through simulations, we demonstrate that HEAL has similar performances to that of Federated Learning in crash-free settings, while being fully decentralized and fault-tolerant. In crash and churn prone environments HEAL outperforms Gossip and Epidemic Learning.

In this paper, we resolve a long-standing open problem in self-stabilization asking whether it is possible to construct a spanning tree using constant memory per node in a synchronous semi-uniform networks, i.e., networks in which one node is distinguished. We design a synchronous self-stabilizing algorithm that constructs a breadth-first search (BFS) tree in any anonymous semi-uniform network using only a constant number of bits of memory per node. Crucially, our approach operates without any prior knowledge of global network parameters such as maximum degree, diameter, or number of nodes. In contrast to traditional self-stabilizing methods - such as pointer-to-neighbors, distance-toroot, or identifiers - that are unsuitable under strict memory constraints, our solution employs an innovative constant-space token dissemination mechanism. This mechanism effectively eliminates cycles and rectifies errors in the BFS structure, ensuring both correctness and memory efficiency. The proposed algorithm not only meets the stringent requirements of memory-constrained distributed systems, but also opens new avenues for research in the design of self-stabilizing protocols under severe resource limitations: constant space-complexity may not systematically prevent the existence of self-stabilizing algorithms for important non-trivial tasks. 2012 ACM Subject Classification Theory of computation -> Design and analysis of algorithms; Mathematics of computing -> Discrete mathematics

Intrusion Detection Systems (IDS) are critical for securing future communication systems, yet existing evaluation methods lack standardization, resulting in incomplete and unreliable assessments. In particular, the evaluation of machine-learning (ML) based IDS often boils down to the demonstration that the IDS performs well on a given dataset, regardless of the dataset quality. Prior evaluation approaches lack formalization and disregard ML best practices. This paper addresses this challenge by presenting FREIDA, a concrete tool for ensuring completeness, reliability, and reproducibility of ML-based IDS evaluations. This tool emphasizes the relationship between evaluation choices and data selection, requiring the generation of purpose-specific datasets. In this paper, we present and provide a Python implementation of our evaluation tool, that is used to evaluate multiple models in a variety of settings. This research represents a crucial stride toward standardizing IDS evaluation methods. Indeed, the proposed tool facilitates the systematic evaluation of IDS by producing a generated configuration file, thereby enhancing the reproducibility of each evaluation.

We consider the problem of graph exploration by energy sharing mobile agents that are subject to crash faults. More precisely, we consider a team of two agents where at most one of them may fail unpredictably, and the considered topology is that of connected acyclic graphs (i.e. trees). We consider both the asynchronous and the synchronous settings, and we provide necessary and sufficient conditions about the energy.

Hierarchical federated learning (HFL) has attracted academic attention to improve the efficiency of federated learning (FL) in real-world applications, however, little research has been done to explore the structural advantages of HFL against Byzantine attacks and to investigate how to make HFL immune to top-level server Single Point of Failure (SPOF). To explore this field and improve the robustness of HFL, we propose a novel generalized paradigm ABD-HFL for asynchronous Byzantine-resistant decentralized hierarchical federated learning, a multi-tier structure without a central server for FL tasks with a large number of devices. Based on the layered structure, an innovative universal Byzantine resistance mechanism is designed in ABD-HFL, which enables it to apply a combination of multiple Byzantine robust techniques, making ABD-HFL more powerful than any single application of such techniques. Besides, ABD-HFL is a fully decentralized HFL, there is no central server, but rather multiple nodes at the top level agree on the global model where malicious model updates are excluded. A new concept of pipeline learning workflow is also introduced to study communication efficiency in ABD-HFL, which is based on asynchronous communication between various levels to train and propagate the global model. Our numerical evaluation validates the advantage of ABD-HFL in terms of robustness and communication efficiency.

Modern distributed systems face growing security threats, as attackers continuously enhance their skills and vulnerabilities span across the entire system stack, from hardware to the application layer. In the system design phase, fault tolerance techniques can be employed to safeguard systems. From a theoretical perspective, an attacker attempting to compromise a system can be abstracted by considering the presence of Byzantine processes in the system. Although this approach enhances the resilience of the distributed system, it introduces certain limitations regarding the accuracy of the model in reflecting real-world scenarios. In this paper, we consider a self-protecting distributed system based on the Monitoring-Analyse-Plan-Execute over a shared Knowledge (MAPE-K) architecture, and we propose a new probabilistic Mobile Byzantine Failure (MBF) that can be plugged into the Analysis component. Our new model captures the dynamics of evolving attacks and can be used to drive the self-protection and reconfiguration strategy. We analyze mathematically the time that it takes until the number of Byzantine nodes crosses given thresholds, or for the system to self-recover back into a safe state, depending on the rates of Byzantine infection spreading vs. the rate of self-recovery. We also provide simulation results that illustrate the behavior of the system under such assumptions.

Recently, a novel peer sampling protocol, Elevator, was introduced to construct network topologies tailored for emerging decentralized applications such as federated learning and blockchain. Elevator builds hub-based topologies in a fully decentralized manner, randomly selecting hubs among participating nodes. These hubs, acting as central nodes connected to the entire network, can be leveraged to accelerate message dissemination. Simulation results have shown that Elevator converges rapidly (within 3–4 cycles) and exhibits robustness against crash failures and churn. However, its resilience to Byzantine adversaries has not been investigated. In this work, we provide the first evaluation of Elevator under Byzantine adversaries and show that even a small fraction (2