Parameterizable Byzantine Broadcast in Loosely Connected Networks

We consider the problem of reliably broadcasting information in a multihop asynchronous network, despite the presence of Byzantine failures: some nodes are malicious and behave arbitrarly. We focus on non-cryptographic solutions. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the good information), but require a highly connected network. A probabilistic approach was recently proposed for loosely connected networks: the Byzantine failures are randomly distributed, and the correct nodes deliver the good information with high probability. A first solution require the nodes to initially know their position on the network, which may be difficult or impossible in self-organizing or dynamic networks. A second solution relaxed this hypothesis but has much weaker Byzantine tolerance guarantees. In this paper, we propose a parameterizable broadcast protocol that does not require nodes to have any knowledge about the network. We give a deterministic technique to compute a set of nodes that always deliver authentic information, for a given set of Byzantine failures. Then, we use this technique to experimentally evaluate our protocol, and show that it significantely outperforms previous solutions with the same hypotheses. Important disclaimer: these results have NOT yet been published in an international conference or journal. This is just a technical report presenting intermediary and incomplete results. A generalized version of these results may be under submission

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

Self-Stabilizing Byzantine-Resilient Communication in Dynamic Networks

We consider the problem of communicating reliably in a dynamic network in the presence of up to k Byzantine failures. It was shown that this problem can be solved if and only if the dynamic graph satisfies a certain condition, that we call "RDC condition". In this paper, we present the first self-stabilizing algorithm for reliable communication in this setting - that is: in addition to permanent Byzantine failures, there can also be an arbitrary number of transient failures. We prove the correctness of this algorithm, provided that the RDC condition is "always eventually satisfied"

Arbitrarily Accurate Aggregation Scheme for Byzantine SGD

A very common optimization technique in Machine Learning is Stochastic Gradient Descent (SGD). SGD can easily be distributed: several workers try to estimate the gradient of a loss function, and a central parameter server gathers these estimates. When all workers behave correctly, the more workers we have, the more accurate the gradient estimate is. We call this the Arbitrary Aggregation Accuracy (AAA) property. However, in practice, some workers may be Byzantine (i.e., have an arbitrary behavior). Interestingly, when a fixed fraction of workers is assumed to be Byzantine (e.g. 20%), no existing aggregation scheme has the AAA property. In this paper, we propose the first aggregation scheme that has this property despite a fixed fraction of Byzantine workers (less than 50%). We theoretically prove this property, and then illustrate it with simulations

Collision-Free Pattern Formation

Shoals of small fishes can change their collective shape and form a specific pattern. They do so efficiently (in parallel) and without collision. In this paper, we study the analog problem of distributed pattern formation. A set of processes needs to move from a set of initial positions to a set of final positions. The processes are oblivious (no internal memory) and must preserve, at any time, a minimal distance between them. A naive solution would be to move the processes one by one, but this would take too long. The difficulty here is to move the processes simultaneously in clearly delimited phases, no matter how unfavorable the initial configuration may be. We solve this by treating the problem "dimension by dimension": the processes first form 1D trails, then gather into a 2D shape (this technique can be generalized to higher dimensions). We present an optimal algorithm which time complexity depends linearly on the radius of the smallest circle containing both initial and final positions. The algorithm is self-stabilizing, as the processes are oblivious and the initial positions are arbitrary

Many-body dispersion effects in the binding of adsorbates on metal surfaces

A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic--inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Phys. Rev. Lett. 108, 236402 (2012); J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid (PTCDA), and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate--surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches