Reliable Communication in a Dynamic Network in the Presence of Byzantine Faults

We consider the following problem: two nodes want to reliably communicate in a dynamic multihop network where some nodes have been compromised, and may have a totally arbitrary and unpredictable behavior. These nodes are called Byzantine. We consider the two cases where cryptography is available and not available. We prove the necessary and sufficient condition (that is, the weakest possible condition) to ensure reliable communication in this context. Our proof is constructive, as we provide Byzantine-resilient algorithms for reliable communication that are optimal with respect to our impossibility results. In a second part, we investigate the impact of our conditions in three case studies: participants interacting in a conference, robots moving on a grid and agents in the subway. Our simulations indicate a clear benefit of using our algorithms for reliable communication in those contexts

Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity

AbstractThis paper presents a distributed algorithm whereby a group of mobile robots self-organize and position themselves into forming a circle in a loosely synchronized environment. In spite of its apparent simplicity, the difficulty of the problem comes from the weak assumptions made on the system. In particular, robots are anonymous, oblivious (i.e., stateless), unable to communicate directly, and disoriented in the sense that they share no knowledge of a common coordinate system. Furthermore, robots’ activations are not synchronized. More specifically, the proposed algorithm ensures that robots deterministically form a non-uniform circle in a finite number of steps and converges to a situation in which all robots are located evenly on the boundary of the circle

A framework for proving the self-organization of dynamic systems

This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize different classes of self-organization through liveness and safety properties that both capture information re- garding the system entropy. We illustrate these classes through study cases. The first ones are two representative P2P overlays (CAN and Pas- try) and the others are specific implementations of \Omega (the leader oracle) and one-shot query abstractions for dynamic settings. Our study aims at understanding the limits and respective power of existing self-organized protocols and lays the basis of designing robust algorithm for dynamic systems

Emergent velocity agreement in robot networks

In this paper we propose and prove correct a new self-stabilizing velocity agreement (flocking) algorithm for oblivious and asynchronous robot networks. Our algorithm allows a flock of uniform robots to follow a flock head emergent during the computation whatever its direction in plane. Robots are asynchronous, oblivious and do not share a common coordinate system. Our solution includes three modules architectured as follows: creation of a common coordinate system that also allows the emergence of a flock-head, setting up the flock pattern and moving the flock. The novelty of our approach steams in identifying the necessary conditions on the flock pattern placement and the velocity of the flock-head (rotation, translation or speed) that allow the flock to both follow the exact same head and to preserve the flock pattern. Additionally, our system is self-healing and self-stabilizing. In the event of the head leave (the leading robot disappears or is damaged and cannot be recognized by the other robots) the flock agrees on another head and follows the trajectory of the new head. Also, robots are oblivious (they do not recall the result of their previous computations) and we make no assumption on their initial position. The step complexity of our solution is O(n)

Agreement-related problems:from semi-passive replication to totally ordered broadcast

Agreement problems constitute a fundamental class of problems in the context of distributed systems. All agreement problems follow a common pattern: all processes must agree on some common decision, the nature of which depends on the specific problem. This dissertation mainly focuses on three important agreements problems: Replication, Total Order Broadcast, and Consensus. Replication is a common means to introduce redundancy in a system, in order to improve its availability. A replicated server is a server that is composed of multiple copies so that, if one copy fails, the other copies can still provide the service. Each copy of the server is called a replica. The replicas must all evolve in manner that is consistent with the other replicas. Hence, updating the replicated server requires that every replica agrees on the set of modifications to carry over. There are two principal replication schemes to ensure this consistency: active replication and passive replication. In Total Order Broadcast, processes broadcast messages to all processes. However, all messages must be delivered in the same order. Also, if one process delivers a message m, then all correct processes must eventually deliver m. The problem of Consensus gives an abstraction to most other agreement problems. All processes initiate a Consensus by proposing a value. Then, all processes must eventually decide the same value v that must be one of the proposed values. These agreement problems are closely related to each other. For instance, Chandra and Toueg [CT96] show that Total Order Broadcast and Consensus are equivalent problems. In addition, Lamport [Lam78] and Schneider [Sch90] show that active replication needs Total Order Broadcast. As a result, active replication is also closely related to the Consensus problem. The first contribution of this dissertation is the definition of the semi-passive replication technique. Semi-passive replication is a passive replication scheme based on a variant of Consensus (called Lazy Consensus and also defined here). From a conceptual point of view, the result is important as it helps to clarify the relation between passive replication and the Consensus problem. In practice, this makes it possible to design systems that react more quickly to failures. The problem of Total Order Broadcast is well-known in the field of distributed systems and algorithms. In fact, there have been already more than fifty algorithms published on the problem so far. Although quite similar, it is difficult to compare these algorithms as they often differ with respect to their actual properties, assumptions, and objectives. The second main contribution of this dissertation is to define five classes of total order broadcast algorithms, and to relate existing algorithms to those classes. The third contribution of this dissertation is to compare the expected performance of the various classes of total order broadcast algorithms. To achieve this goal, we define a set of metrics to predict the performance of distributed algorithms

Understanding the Power of Stigmergy of Anonymous Agents in Discrete Environments

International audienceCommunication by stigmergy consists, for agents/robots devoid of other dedicated communication devices, in exchanging information by observing each other's movements, similar to how honeybees use a dance to inform each other on the location of food sources. Stigmergy, while a popular technique in soft computing (e.g., swarm intelligence and swarm robotics), has received little attention from a computational viewpoint, with only one study proposing a method in a continuous environment. An important question is whether there are limits intrinsic to the environment on the feasibility of stigmergy. While it is not the case in a continuous environment, we show that the answer is quite different when the environment is discrete. This paper considers stigmergy in graphs and identifies classes of graphs in which robots can communicate by stigmergy. We provide two algorithms with different tradeoffs. One algorithm achieves faster stigmergy when the density of robots is low enough to let robots move independently. This algorithm works when the graph contains some particular pairwise-disjoint subgraphs. The second algorithm, while slower solves the problem under an extremely high density of robots assuming that the graph admits some large cycle. Both algorithms are described in a general way, for any graph that admits the desired properties and with identified nodes. We show how the latter assumption can be removed in more specific topologies. Indeed, we consider stigmergy in the grid which offers additional orientation information not available in a general graphs, allowing us to relax some of the assumptions. Given an $N\times M$ anonymous grid, we show that the first algorithm requires $O(\mathcal{M})$ steps to achieve communication by stigmergy, where $\mathcal{M}$ is the maximum length of a communication message, but it works only if the number of robots is less than $\left\lfloor\frac{N\cdot M}{9}\right\rfloor$. The second algorithm, which requires $O(k^2)$ steps, where $k$ is the number of robots, on the other hand, works for up to $N\cdot M-5$ robots. In both cases, we consider very weak assumptions on the robots capabilities: i.e., we assume that the robots are anonymous, asynchronous, uniform, and execute deterministic algorithms

Time-Independent Planning for Multiple Moving Agents

Typical Multi-agent Path Finding (MAPF) solvers assume that agents move synchronously, thus neglecting the reality gap in timing assumptions, e.g., delays caused by an imperfect execution of asynchronous moves. So far, two policies enforce a robust execution of MAPF plans taken as input: either by forcing agents to synchronize or by executing plans while preserving temporal dependencies. This paper proposes an alternative approach, called time-independent planning, which is both online and distributed. We represent reality as a transition system that changes configurations according to atomic actions of agents, and use it to generate a time-independent schedule. Empirical results in a simulated environment with stochastic delays of agents' moves support the validity of our proposal.Comment: 10 pages, 5 figures, to be presented at AAAI-21, Feb 2021, Virtual Conferenc

Specification of Replication Techniques, Semi-Passive Replication, and Lazy consensus*

This paper brings the following three main contributions: a hierarchy of specifications for replication techniques, semi-passive replication, and Lazy Consensus. Based on the definition of the Generic Replication problem, we difine two families of replication techniques: replication with parsimonious processing (e.g., passive replication), and replication with redundant processing (e.g., active replication). This helps relate replication techniques to each other. We define a novel replication technique with parsimonious processing, called semi-passive replication, for which we also give an algorithm. The most significant aspect of semi-passive replication is that it requires a weaker system model than existing techniques of the same family. We difine a variant of the Consensus problem, called Lazy Consensus, upon which our semi-passive replication algorithm is based. The main difference between Consensus and Lazy Consensus is a property of laziness which requires that initial values are computed only when they are actually needed