Avatar: A Time- and Space-Efficient Self-Stabilizing Overlay Network

Overlay networks present an interesting challenge for fault-tolerant computing. Many overlay networks operate in dynamic environments (e.g. the Internet), where faults are frequent and widespread, and the number of processes in a system may be quite large. Recently, self-stabilizing overlay networks have been presented as a method for managing this complexity. \emph{Self-stabilizing overlay networks} promise that, starting from any weakly-connected configuration, a correct overlay network will eventually be built. To date, this guarantee has come at a cost: nodes may either have high degree during the algorithm's execution, or the algorithm may take a long time to reach a legal configuration. In this paper, we present the first self-stabilizing overlay network algorithm that does not incur this penalty. Specifically, we (i) present a new locally-checkable overlay network based upon a binary search tree, and (ii) provide a randomized algorithm for self-stabilization that terminates in an expected polylogarithmic number of rounds \emph{and} increases a node's degree by only a polylogarithmic factor in expectation

Tight Bounds for MIS in Multichannel Radio Networks

Daum et al. [PODC'13] presented an algorithm that computes a maximal independent set (MIS) within $O(\log^2 n/F+\log n \mathrm{polyloglog} n)$ rounds in an $n$-node multichannel radio network with $F$ communication channels. The paper uses a multichannel variant of the standard graph-based radio network model without collision detection and it assumes that the network graph is a polynomially bounded independence graph (BIG), a natural combinatorial generalization of well-known geographic families. The upper bound of that paper is known to be optimal up to a polyloglog factor. In this paper, we adapt algorithm and analysis to improve the result in two ways. Mainly, we get rid of the polyloglog factor in the runtime and we thus obtain an asymptotically optimal multichannel radio network MIS algorithm. In addition, our new analysis allows to generalize the class of graphs from those with polynomially bounded local independence to graphs where the local independence is bounded by an arbitrary function of the neighborhood radius.Comment: 37 pages, to be published in DISC 201

Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log \Delta)$ bits per node and $O(nD)$ respectively, where $\Delta$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay '94 -- in the model, an omniscient adversary can corrupt up to $f$ nodes in each round, and at the beginning of each round, faults may "move" in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a simple iterative approximate consensus algorithm which requires at least $4f+1$ nodes. This paper proposes a novel technique of using "confession" (a mechanism to allow others to ignore past behavior) and a variant of reliable broadcast to improve the fault-tolerance level. In particular, we present an approximate consensus algorithm that requires only $\lceil 7f/2\rceil + 1$ nodes, an $\lfloor f/2 \rfloor$ improvement over the state-of-the-art algorithms. Moreover, we also show that the proposed algorithm is optimal within a family of round-based algorithms

Grover's Quantum Search Algorithm and Diophantine Approximation

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change

Self-stabilizing virtual synchrony

Virtual synchrony (VS) is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is critical for the success of such implementations since large distributed systems can be highly available as long as they do not depend on the full operational status of every system participant. Self-stabilizing systems can tolerate transient faults that drive the system to an arbitrary unpredictable configuration. Such systems automatically regain consistency from any such configuration, and then produce the desired system behavior ensuring it for practically infinite number of successive steps, e.g., 264 steps. We present a new multi-purpose self-stabilizing counter algorithm establishing an efficient practically unbounded counter, that can directly yield a self-stabilizing Multiple-Writer Multiple-Reader (MWMR) register emulation. We use our counter algorithm, together with a selfstabilizing group membership and a self-stabilizing multicast service to devise the first practically stabilizing VS algorithm and a self-stabilizing VS-based emulation of state machine replication (SMR). As we base the SMR implementation on VS, rather than consensus, the system progresses in more extreme asynchronous settings in relation to consensusbased SMR

Local Charge of the nu=5/2 Fractional Quantum Hall State

Electrons in two dimensions and strong magnetic fields effectively lose their kinetic energy and display exotic behavior dominated by Coulomb forces. When the ratio of electrons to magnetic flux quanta in the system is near 5/2, the unique correlated phase that emerges is predicted to be gapped with fractionally charged quasiparticles and a ground state degeneracy that grows exponentially as these quasiparticles are introduced. Interestingly, the only way to transform between the many ground states would be to braid the fractional excitations around each other, a property with applications in quantum information processing. Here we present the first observation of localized quasiparticles at nu=5/2, confined to puddles by disorder. Using a local electrometer to compare how quasiparticles at nu=5/2 and nu=7/3 charge these puddles, we are able to extract the ratio of local charges for these states. Averaged over several disorder configurations and samples, we find the ratio to be 4/3, suggesting that the local charges are e/3 at seven thirds and e/4 at five halves, in agreement with theoretical predictions. This confirmation of localized e/4 quasiparticles is necessary for proposed interferometry experiments to test statistics and computational ability of the state at nu=5/2.Comment: 6 pages, 4 figures corrected titl

Peer-to-Peer Secure Multi-Party Numerical Computation Facing Malicious Adversaries

We propose an efficient framework for enabling secure multi-party numerical computations in a Peer-to-Peer network. This problem arises in a range of applications such as collaborative filtering, distributed computation of trust and reputation, monitoring and other tasks, where the computing nodes is expected to preserve the privacy of their inputs while performing a joint computation of a certain function. Although there is a rich literature in the field of distributed systems security concerning secure multi-party computation, in practice it is hard to deploy those methods in very large scale Peer-to-Peer networks. In this work, we try to bridge the gap between theoretical algorithms in the security domain, and a practical Peer-to-Peer deployment. We consider two security models. The first is the semi-honest model where peers correctly follow the protocol, but try to reveal private information. We provide three possible schemes for secure multi-party numerical computation for this model and identify a single light-weight scheme which outperforms the others. Using extensive simulation results over real Internet topologies, we demonstrate that our scheme is scalable to very large networks, with up to millions of nodes. The second model we consider is the malicious peers model, where peers can behave arbitrarily, deliberately trying to affect the results of the computation as well as compromising the privacy of other peers. For this model we provide a fourth scheme to defend the execution of the computation against the malicious peers. The proposed scheme has a higher complexity relative to the semi-honest model. Overall, we provide the Peer-to-Peer network designer a set of tools to choose from, based on the desired level of security.Comment: Submitted to Peer-to-Peer Networking and Applications Journal (PPNA) 200

Understanding Autoimmune Mechanisms in Multiple Sclerosis Using Gene Expression Microarrays: Treatment Effect and Cytokine-related Pathways

Multiple sclerosis (MS) is a central nervous system disease in which activated autoreactive T-cells invade the blood brain barrier and initiate an inflammatory response that leads to myelin destruction and axonal loss. The etiology of MS, as well as the mechanisms associated with its unexpected onset, the unpredictable clinical course spanning decades, and the different rates of progression leading to disability over time, remains an enigma. We have applied gene expression microarrays technology in peripheral blood mononuclear cells (PBMC) to better understand MS pathogenesis and better target treatment approaches. A signature of 535 genes were found to distinguish immunomodulatory treatment effects between 13 treated and 13 untreated MS patients. In addition, the expression pattern of 1109 gene transcripts that were previously reported to significantly differentiate between MS patients and healthy subjects were further analyzed to study the effect of cytokine-related pathways on disease pathogenesis. When relative gene expression for 26 MS patients was compared to 18 healthy controls, 30 genes related to various cytokine-associated pathways were identified. These genes belong to a variety of families such as interleukins, small inducible cytokine subfamily and tumor necrosis factor ligand and receptor. Further analysis disclosed seven cytokine-associated genes within the immunomodulatory treatment signature, and two cytokine-associated genes SCYA4 (small inducible cytokine A4) and FCAR (Fc fragment of IgA, CD89) that were common to both the MS gene expression signature and the immunomodulatory treatment gene expression signature. Our results indicate that cytokine-associated genes are involved in various pathogenic pathways in MS and also related to immunomodulatory treatment effects