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Sébastien Tixeuil

Publications and source records attributed to Sébastien Tixeuil.

At least 19 recordsLinked to original sources
arXiv2026

An Asynchronous Maximum Independent Set Algorithm by Myopic Luminous Robots on Grids

We consider the problem of constructing a maximum independent set with mobile myopic luminous robots on a grid network whose size is finite but unknown to the robots. In this setting, the robots enter the grid network one-by-one from a corner of the grid, and they eventually have to be disseminated on the grid nodes so that the occupied positions form a maximum independent set of the network. We assume that robots are asynchronous, anonymous, silent, and they execute the same distributed algorithm. In this paper, we propose two algorithms: The first one assumes the number of light colors of each robot is three and the visible range is two, but uses additional strong assumptions of port-numbering for each node. To delete this assumption, the second one assumes the number of light colors of each robot is seven and the visible range is three. In both algorithms, the number of movements is $O(n(L+l))$ steps where $n$ is the number of nodes and $L$ and $l$ are the grid dimensions.

cs.DC↗
arXiv2026

Deterministic Self-Stabilizing BFS Construction in Constant Space

In this paper, we resolve a long-standing question in self-stabilization by demonstrating that it is indeed possible to construct a spanning tree in a semi-uniform network using constant memory per node. We introduce a self-stabilizing synchronous algorithm that builds a breadth-first search (BFS) spanning tree with only $O(1)$ bits of memory per node, converging in $2^ε$ time units, where $ε$ denotes the eccentricity of the distinguish node. Crucially, our approach operates without any prior knowledge of global network parameters such as maximum degree, diameter, or total node count. In contrast to traditional self-stabilizing methods, such as pointer-to-neighbor communication or distance-to-root computation, that are unsuitable under strict memory constraints, our solution employs an innovative constant-space token dissemination mechanism. This mechanism effectively eliminates cycles and rectifies deviations 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 self-stabilizing protocols under severe resource limitations.

cs.DC↗
arXiv2026

Hardwired Pattern Formation by Mobile Robots with Common Unit Distance

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.

cs.DC↗
arXiv2026

On the Solvability of Byzantine-tolerant Reliable Communication in Dynamic Networks

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.

cs.DC↗
arXiv2026

HEAL: Resilient and Self-* Hub-based Learning

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.

cs.LG↗
arXiv2026

Tight Bounds on Window Size and Time for Single-Agent Graph Exploration under T-Interval Connectivity

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 $O(ε(n,m)\cdot m + n \log^2 n)$, where $ε(n,m) = \frac{\ln n}{1 + \ln m - \ln n}$. 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 $KT_1$.

cs.DC↗
arXiv2026

The Price of Universal Temporal Reachability

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.

cs.DS↗
arXiv2026

Emergent Peer-to-Peer Multi-Hub Topology

In this paper we propose and evaluate an innovative algorithm that enables the creation of Peer-to-Peer network overlays characterized by emergent multi-hubs. This approach generates overlays that balance between the randomness of a graph and the structure of a star network, resulting in networks that not only feature prominent hubs but also exhibit strong resilience to failures. By leveraging principles of preferential attachment and random attachment, our method allows hubs to form spontaneously, offering a decentralized and fault-tolerant solution ideal for applications requiring both low network diameter and high robustness. The protocol is entirely decentralized, operates asynchronously, and depends exclusively on local information. Nodes organically evolve into hubs and remain indistinguishable from other nodes (except in terms of the number of incoming links). The quantity of hubs that emerge can be predetermined by the application as a network parameter.

cs.DC↗
arXiv2026

LIFT: Byzantine Resilient Hub-Sampling

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%) of Byzantine nodes is sufficient to subvert the network. As a result, we introduce LIFT, a new protocol that extends Elevator by employing a cryptographically secure pseudo-random number generator (PRNG) for hub selection, thereby mitigating Byzantine manipulation. In contrast, LIFT withstands adversarial infiltration and remains robust with up to 10% Byzantine nodes. These results highlight the necessity of secure randomness in decentralized hub formation and position LIFT as a more reliable building block for Byzantine-resilient decentralized systems.

cs.CR↗
arXiv2024

Data Poisoning Attacks in Gossip Learning

Traditional machine learning systems were designed in a centralized manner. In such designs, the central entity maintains both the machine learning model and the data used to adjust the model's parameters. As data centralization yields privacy issues, Federated Learning was introduced to reduce data sharing and have a central server coordinate the learning of multiple devices. While Federated Learning is more decentralized, it still relies on a central entity that may fail or be subject to attacks, provoking the failure of the whole system. Then, Decentralized Federated Learning removes the need for a central server entirely, letting participating processes handle the coordination of the model construction. This distributed control urges studying the possibility of malicious attacks by the participants themselves. While poisoning attacks on Federated Learning have been extensively studied, their effects in Decentralized Federated Learning did not get the same level of attention. Our work is the first to propose a methodology to assess poisoning attacks in Decentralized Federated Learning in both churn free and churn prone scenarios. Furthermore, in order to evaluate our methodology on a case study representative for gossip learning we extended the gossipy simulator with an attack injector module.

cs.DC↗
arXiv2024

Practical Byzantine Reliable Broadcast on Partially Connected Networks (Extended version)

In this paper, we consider the Byzantine reliable broadcast problem on authenticated and partially connected networks. The state-of-the-art method to solve this problem consists in combining two algorithms from the literature. Handling asynchrony and faulty senders is typically done thanks to Gabriel Bracha's authenticated double-echo broadcast protocol, which assumes an asynchronous fully connected network. Danny Dolev's algorithm can then be used to provide reliable communications between processes in the global fault model, where up to f processes among N can be faulty in a communication network that is at least 2f+1-connected. Following recent works that showed that Dolev's protocol can be made more practical thanks to several optimizations, we show that the state-of-the-art methods to solve our problem can be optimized thanks to layer-specific and cross-layer optimizations. Our simulations with the Omnet++ network simulator show that these optimizations can be efficiently combined to decrease the total amount of information transmitted or the protocol's latency (e.g., respectively, -25% and -50% with a 16B payload, N=31 and f=4) compared to the state-of-the-art combination of Bracha's and Dolev's protocols.

cs.DC↗
arXiv2024

Stand-Up Indulgent Gathering on Rings

We consider a collection of $k \geq 2$ robots that evolve in a ring-shaped network without common orientation, and address a variant of the crash-tolerant gathering problem called the \emph{Stand-Up Indulgent Gathering} (SUIG): given a collection of robots, if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in finite time; if one robot or more robots crash on the same location, the remaining correct robots gather at the location of the crashed robots. We aim at characterizing the solvability of the SUIG problem without multiplicity detection capability.

cs.DC↗
arXiv2024

Stand-Up Indulgent Gathering on Lines for Myopic Luminous Robots

We consider a strong variant of the crash fault-tolerant gathering problem called stand-up indulgent gathering (SUIG), by robots endowed with limited visibility sensors and lights on line-shaped networks. In this problem, a group of mobile robots must eventually gather at a single location, not known beforehand, regardless of the occurrence of crashes. Differently from previous work that considered unlimited visibility, we assume that robots can observe nodes only within a certain fixed distance (that is, they are myopic), and emit a visible color from a fixed set (that is, they are luminous), without multiplicity detection. We consider algorithms depending on two parameters related to the initial configuration: $M_{init}$, which denotes the number of nodes between two border nodes, and $O_{init}$, which denotes the number of nodes hosting robots. Then, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if $M_{init}$ or $O_{init}$ is odd, SUIG can be solved in the fully synchronous model.

cs.DC↗
arXiv2023

Constrained Backward Time Travel Planning is in P

We consider transportation networks that are modeled by dynamic graphs, and introduce the possibility for traveling agents to use Backward Time-Travel (BTT) devices at any node to go back in time (to some extent, and with some appropriate fee) before resuming their trip. We focus on dynamic line graphs. In more detail, we propose exact algorithms to compute travel plans with constraints on the BTT cost or on how far back in time you can go, while minimizing travel delay (that is, the time difference between the arrival instant and the starting instant), in polynomial time. We study the impact of the BTT devices pricing policies on the computation process of those plans considering travel delay and cost, and provide necessary properties that pricing policies should satisfy to enable to compute such plans. Finally, we provide an optimal online algorithm for the unconstrained problem when the cost function is the identity.

cs.CC↗
arXiv2023

Reliable Broadcast despite Mobile Byzantine Faults

We investigate the solvability of the Byzantine Reliable Broadcast and Byzantine Broadcast Channel problems in distributed systems affected by Mobile Byzantine Faults. We show that both problems are not solvable even in one of the most constrained system models for mobile Byzantine faults defined so far. By endowing processes with an additional local failure oracle, we provide a solution to the Byzantine Broadcast Channel problem.

cs.DC↗
arXiv2023

Meeting Times of Non-atomic Random Walks

In this paper, we revisit the problem of classical \textit{meeting times} of random walks in graphs. In the process that two tokens (called agents) perform random walks on an undirected graph, the meeting times are defined as the expected times until they meet when the two agents are initially located at different vertices. A key feature of the problem is that, in each discrete time-clock (called \textit{round}) of the process, the scheduler selects only one of the two agents, and the agent performs one move of the random walk. In the adversarial setting, the scheduler utilizes the strategy that intends to \textit{maximizing} the expected time to meet. In the seminal papers \cite{collisions,israeli1990token,tetali1993simult}, for the random walks of two agents, the notion of \textit{atomicity} is implicitly considered. That is, each move of agents should complete while the other agent waits. In this paper, we consider and formalize the meeting time of \textit{non-atomic} random walks. In the non-atomic random walks, we assume that in each round, only one agent can move but the move does not necessarily complete in the next round. In other words, we assume that an agent can move at a round while the other agent is still moving on an edge. For the non-atomic random walks with the adversarial schedulers, we give a polynomial upper bound on the meeting times.

cs.DC↗
arXiv2023

Stand-Up Indulgent Gathering on Lines

We consider a variant of the crash-fault gathering problem called stand-up indulgent gathering (SUIG). In this problem, a group of mobile robots must eventually gather at a single location, which is not known in advance. If no robots crash, they must all meet at the same location. However, if one or more robots crash at a single location, all non-crashed robots must eventually gather at that location. The SUIG problem was first introduced for robots operating in a two-dimensional continuous Euclidean space, with most solutions relying on the ability of robots to move a prescribed (real) distance at each time instant. In this paper, we investigate the SUIG problem for robots operating in a discrete universe (i.e., a graph) where they can only move one unit of distance (i.e., to an adjacent node) at each time instant. Specifically, we focus on line-shaped networks and characterize the solvability of the SUIG problem for oblivious robots without multiplicity detection.

cs.DC↗
arXiv2023

Stand Up Indulgent Gathering

We consider a swarm of mobile robots evolving in a bidimensional Euclidean space. We study a variant of the crash-tolerant gathering problem: if no robot crashes, robots have to meet at the same arbitrary location, not known beforehand, in finite time; if one or several robots crash at the same location, the remaining correct robots gather at the crash location to rescue them. Motivated by impossibility results in the semi-synchronous setting, we present the first solution to the problem for the fully synchronous setting that operates in the vanilla Look-Compute-Move model with no additional hypotheses: robots are oblivious, disoriented, have no multiplicity detection capacity, and may start from arbitrary positions (including those with multiplicity points). We furthermore show that robots gather in a time that is proportional to the initial maximum distance between robots.

cs.DC↗