arXiv subjects

Danny Dolev

Publications and source records attributed to Danny Dolev.

43 records · Page 3Linked to original sources

arXiv2008

Gaussian Belief Propagation for Solving Systems of Linear Equations: Theory and Application

The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation (GaBP) that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed message-passing implementation of the solution algorithm. We address the properties of the GaBP solver, including convergence, exactness, computational complexity, message-passing efficiency and its relation to classical solution methods. We use numerical examples and applications, like linear detection, to illustrate these properties through the use of computer simulations. This empirical study demonstrates the attractiveness (e.g., faster convergence rate) of the proposed GaBP solver in comparison to conventional linear-algebraic iterative solution methods.

cs.IT↗

arXiv2008

An Almost-Surely Terminating Polynomial Protocol for Asynchronous Byzantine Agreement with Optimal Resilience

Consider an asynchronous system with private channels and $n$ processes, up to $t$ of which may be faulty. We settle a longstanding open question by providing a Byzantine agreement protocol that simultaneously achieves three properties: 1. (optimal) resilience: it works as long as $n>3t$ 2. (almost-sure) termination: with probability one, all nonfaulty processes terminate 3. (polynomial) efficiency: the expected computation time, memory consumption, message size, and number of messages sent are all polynomial in $n$. Earlier protocols have achieved only two of these three properties. In particular, the protocol of Bracha is not polynomially efficient, the protocol of Feldman and Micali is not optimally resilient, and the protocol of Canetti and Rabin does not have almost-sure termination. Our protocol utilizes a new primitive called shunning (asynchronous) verifiable secret sharing (SVSS), which ensures, roughly speaking, that either a secret is successfully shared or a new faulty process is ignored from this point onwards by some nonfaulty process.

cs.DC↗

arXiv2008

Self-Stabilizing Pulse Synchronization Inspired by Biological Pacemaker Networks

We define the ``Pulse Synchronization'' problem that requires nodes to achieve tight synchronization of regular pulse events, in the settings of distributed computing systems. Pulse-coupled synchronization is a phenomenon displayed by a large variety of biological systems, typically overcoming a high level of noise. Inspired by such biological models, a robust and self-stabilizing Byzantine pulse synchronization algorithm for distributed computer systems is presented. The algorithm attains near optimal synchronization tightness while tolerating up to a third of the nodes exhibiting Byzantine behavior concurrently. Pulse synchronization has been previously shown to be a powerful building block for designing algorithms in this severe fault model. We have previously shown how to stabilize general Byzantine algorithms, using pulse synchronization. To the best of our knowledge there is no other scheme to do this without the use of synchronized pulses.

cs.DC↗

arXiv2007

Lower Bounds on Implementing Robust and Resilient Mediators

We consider games that have (k,t)-robust equilibria when played with a mediator, where an equilibrium is (k,t)-robust if it tolerates deviations by coalitions of size up to k and deviations by up to $t$ players with unknown utilities. We prove lower bounds that match upper bounds on the ability to implement such mediators using cheap talk (that is, just allowing communication among the players). The bounds depend on (a) the relationship between k, t, and n, the total number of players in the system; (b) whether players know the exact utilities of other players; (c) whether there are broadcast channels or just point-to-point channels; (d) whether cryptography is available; and (e) whether the game has a $k+t)-punishment strategy; that is, a strategy that, if used by all but at most $k+t$ players, guarantees that every player gets a worse outcome than they do with the equilibrium strategy.

cs.GT↗

arXiv2006

Self-Stabilizing Byzantine Pulse Synchronization

The ``Pulse Synchronization'' problem can be loosely described as targeting to invoke a recurring distributed event as simultaneously as possible at the different nodes and with a frequency that is as regular as possible. This target becomes surprisingly subtle and difficult to achieve when facing both transient and permanent failures. In this paper we present an algorithm for pulse synchronization that self-stabilizes while at the same time tolerating a permanent presence of Byzantine faults. The Byzantine nodes might incessantly try to de-synchronize the correct nodes. Transient failures might throw the system into an arbitrary state in which correct nodes have no common notion what-so-ever, such as time or round numbers, and can thus not infer anything from their own local states upon the state of other correct nodes. The presented algorithm grants nodes the ability to infer that eventually all correct nodes will invoke their pulses within a very short time interval of each other and will do so regularly. Pulse synchronization has previously been shown to be a powerful tool for designing general self-stabilizing Byzantine algorithms and is hitherto the only method that provides for the general design of efficient practical protocols in the confluence of these two fault models. The difficulty, in general, to design any algorithm in this fault model may be indicated by the remarkably few algorithms resilient to both fault models. The few published self-stabilizing Byzantine algorithms are typically complicated and sometimes converge from an arbitrary initial state only after exponential or super exponential time.

cs.DC↗

arXiv2006

Linear-time Self-stabilizing Byzantine Clock Synchronization

Clock synchronization is a very fundamental task in distributed system. It thus makes sense to require an underlying clock synchronization mechanism to be highly fault-tolerant. A self-stabilizing algorithm seeks to attain synchronization once lost; a Byzantine algorithm assumes synchronization is never lost and focuses on containing the influence of the permanent presence of faulty nodes. There are efficient self-stabilizing solutions for clock synchronization as well as efficient solutions that are resilient to Byzantine faults. In contrast, to the best of our knowledge there is no practical solution that is self-stabilizing while tolerating the permanent presence of Byzantine nodes. We present the first linear-time self-stabilizing Byzantine clock synchronization algorithm. Our deterministic clock synchronization algorithm is based on the observation that all clock synchronization algorithms require events for exchanging clock values and re-synchronizing the clocks to within safe bounds. These events usually need to happen synchronously at the different nodes. In classic Byzantine algorithms this is fulfilled or aided by having the clocks initially close to each other and thus the actual clock values can be used for synchronizing the events. This implies that clock values cannot differ arbitrarily, which necessarily renders these solutions to be non-stabilizing. Our scheme suggests using an underlying distributed pulse synchronization module that is uncorrelated to the clock values.

cs.DC↗

arXiv2006

Search in Complex Networks : a New Method of Naming

We suggest a method for routing when the source does not posses full information about the shortest path to the destination. The method is particularly useful for scale-free networks, and exploits its unique characteristics. By assigning new (short) names to nodes (aka labelling) we are able to reduce significantly the memory requirement at the routers, yet we succeed in routing with high probability through paths very close in distance to the shortest ones.

cs.NI↗