arXiv subjects

Shlomi Dolev

Publications and source records attributed to Shlomi Dolev.

At least 55 records · Page 3Linked to original sources

arXiv2015

Stabilizing Server-Based Storage in Byzantine Asynchronous Message-Passing Systems

A stabilizing Byzantine single-writer single-reader (SWSR) regular register, which stabilizes after the first invoked write operation, is first presented. Then, new/old ordering inversions are eliminated by the use of a (bounded) sequence number for writes, obtaining a practically stabilizing SWSR atomic register. A practically stabilizing Byzantine single-writer multi-reader (SWMR) atomic register is then obtained by using several copies of SWSR atomic registers. Finally, bounded time-stamps, with a time-stamp per writer, together with SWMR atomic registers, are used to construct a practically stabilizing Byzantine multi-writer multi-reader (MWMR) atomic register. In a system of $n$ servers implementing an atomic register, and in addition to transient failures, the constructions tolerate t<n/8 Byzantine servers if communication is asynchronous, and t<n/3 Byzantine servers if it is synchronous. The noteworthy feature of the proposed algorithms is that (to our knowledge) these are the first that build an atomic read/write storage on top of asynchronous servers prone to transient failures, and where up to t of them can be Byzantine.

cs.DC↗

arXiv2015

Assignment of Different-Sized Inputs in MapReduce

A MapReduce algorithm can be described by a mapping schema, which assigns inputs to a set of reducers, such that for each required output there exists a reducer that receives all the inputs that participate in the computation of this output. Reducers have a capacity, which limits the sets of inputs that they can be assigned. However, individual inputs may vary in terms of size. We consider, for the first time, mapping schemas where input sizes are part of the considerations and restrictions. One of the significant parameters to optimize in any MapReduce job is communication cost between the map and reduce phases. The communication cost can be optimized by minimizing the number of copies of inputs sent to the reducers. The communication cost is closely related to the number of reducers of constrained capacity that are used to accommodate appropriately the inputs, so that the requirement of how the inputs must meet in a reducer is satisfied. In this work, we consider a family of problems where it is required that each input meets with each other input in at least one reducer. We also consider a slightly different family of problems in which, each input of a set, X, is required to meet each input of another set, Y, in at least one reducer. We prove that finding an optimal mapping schema for these families of problem is NP-hard, and present several approximation algorithms for finding a near optimal mapping schema.

cs.DB↗

arXiv2013

Fast Self-Stabilizing Minimum Spanning Tree Construction Using Compact Nearest Common Ancestor Labeling Scheme

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor $Θ(n)$, to the price of increasing the best known space complexity by a factor $O(\log n)$. The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only $O(\log^2n)$ bits.

cs.DC↗

arXiv2013

Ameba-inspired Self-organizing Particle Systems

Particle systems are physical systems of simple computational particles that can bond to neighboring particles and use these bonds to move from one spot to another (non-occupied) spot. These particle systems are supposed to be able to self-organize in order to adapt to a desired shape without any central control. Self-organizing particle systems have many interesting applications like coating objects for monitoring and repair purposes and the formation of nano-scale devices for surgery and molecular-scale electronic structures. While there has been quite a lot of systems work in this area, especially in the context of modular self-reconfigurable robotic systems, only very little theoretical work has been done in this area so far. We attempt to bridge this gap by proposing a model inspired by the behavior of ameba that allows rigorous algorithmic research on self-organizing particle systems.

cs.DC↗

arXiv2013

Self-Stabilizing Paxos

We present the first self-stabilizing consensus and replicated state machine for asynchronous message passing systems. The scheme does not require that all participants make a certain number of steps prior to reaching a practically infinite execution where the replicated state machine exhibits the desired behavior. In other words, the system reaches a configuration from which it operates according to the specified requirements of the replicated state-machine, for a long enough execution regarding all practical considerations.

cs.DC↗

arXiv2013

Self-Stabilizing Byzantine Resilient Topology Discovery and Message Delivery

Traditional Byzantine resilient algorithms use 2f+1 vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task, dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We present the first such algorithm that can cope with Byzantine nodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node is eventually aware of all the other non-Byzantine nodes and their connecting communication links. Using the topology information, nodes can, for example, route messages across the network and deliver messages from one end user to another. We present the first deterministic, cryptographicassumptions- free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery and end-to-end message delivery. We also consider the task of r-neighborhood discovery for the case in which r and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facilitates polynomial time, communication and space solutions for the above tasks. The obtained algorithms can be used to authenticate parties, in particular during the establishment of private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of the compromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on the established private secrets can be employed in between periodical re-establishments of the secrets.

cs.DC↗

arXiv2012

Data Interpolation: An Efficient Sampling Alternative for Big Data Aggregation

Given a large set of measurement sensor data, in order to identify a simple function that captures the essence of the data gathered by the sensors, we suggest representing the data by (spatial) functions, in particular by polynomials. Given a (sampled) set of values, we interpolate the datapoints to define a polynomial that would represent the data. The interpolation is challenging, since in practice the data can be noisy and even Byzantine, where the Byzantine data represents an adversarial value that is not limited to being close to the correct measured data. We present two solutions, one that extends the Welch-Berlekamp technique in the case of multidimensional data, and copes with discrete noise and Byzantine data, and the other based on Arora and Khot techniques, extending them in the case of multidimensional noisy and Byzantine data.

cs.NI↗

arXiv2012

Efficient Private Distributed Computation on Unbounded Input Streams

In the problem of swarm computing, $n$ agents wish to securely and distributively perform a computation on common inputs, in such a way that even if the entire memory contents of some of them are exposed, no information is revealed about the state of the computation. Recently, Dolev, Garay, Gilboa and Kolesnikov [ICS 2011] considered this problem in the setting of information-theoretic security, showing how to perform such computations on input streams of unbounded length. The cost of their solution, however, is exponential in the size of the Finite State Automaton (FSA) computing the function. In this work we are interested in efficient computation in the above model, at the expense of minimal additional assumptions. Relying on the existence of one-way functions, we show how to process a priori unbounded inputs (but of course, polynomial in the security parameter) at a cost linear in $m$, the number of FSA states. In particular, our algorithms achieve the following: * In the case of $(n,n)$-reconstruction (i.e. in which all $n$ agents participate in reconstruction of the distributed computation) and at most $n-1$ agents are corrupted, the agent storage, the time required to process each input symbol and the time complexity for reconstruction are all $O(mn)$. * In the case of $(t+1,n)$-reconstruction (where only $t+1$ agents take part in the reconstruction) and at most $t$ agents are corrupted, the agents' storage and time required to process each input symbol are $O(m{n-1 \choose t-1})$. The complexity of reconstruction is $O(m(t+1))$.

cs.DC↗

arXiv2012

Optical Solver of Combinatorial Problems: Nano-Technological Approach

We report the first steps in creating an optical computing system. This system may solve NP-Hard problems by utilizing a setup of exponential sized masks. This is exponential space complexity but the production of those masks is done with a polynomial time preprocessing. These masks are later used to solve the problem in polynomial time. We propose to reduced the size of the masks to nano-scaled density. Simulations were done to choose a proper design, and actual implementations show the feasibility of such a system.

cs.ET↗

arXiv2011

Efficient and Universal Corruption Resilient Fountain Codes

In this paper, we present a new family of fountain codes which overcome adversarial errors. That is, we consider the possibility that some portion of the arriving packets of a rateless erasure code are corrupted in an undetectable fashion. In practice, the corrupted packets may be attributed to a portion of the communication paths which are controlled by an adversary or to a portion of the sources that are malicious. The presented codes resemble and extend LT and Raptor codes. Yet, their benefits over existing coding schemes are manifold. First, to overcome the corrupted packets, our codes use information theoretic techniques, rather than cryptographic primitives. Thus, no secret channel between the senders and the receivers is required. Second, the encoders in the suggested scheme are oblivious to the strength of the adversary, yet perform as if its strength was known in advance. Third, the sparse structure of the codes facilitates efficient decoding. Finally, the codes easily fit a decentralized scenario with several sources, when no communication between the sources is allowed. We present both exhaustive as well as efficient decoding rules. Beyond the obvious use as a rateless codes, our codes have important applications in distributed computing.

cs.IT↗

arXiv2011

Communication Optimalement Stabilisante sur Canaux non Fiables et non FIFO

A self-stabilizing protocol has the capacity to recover a legitimate behavior whatever is its initial state. The majority of works in self-stabilization assume a shared memory model or a communication using reliable and FIFO channels. In this article, we interest in self-stabilizing systems using bounded but non reliable and non FIFO channels. We propose a stabilizing communication protocol with optimal fault resilience. In more details, this protocol simulates a reliable and FIFO channel and ensures a minimal number of looses, duplications, creations, and re-ordering of messages.

cs.DC↗

arXiv2011

Computer Arithmetic Preserving Hamming Distance of Operands in Operation Result

The traditional approach to fault tolerant computing involves replicating computation units and applying a majority vote operation on individual result bits. This approach, however, has several limitations; the most severe is the resource requirement. This paper presents a new method for fault tolerant computing where for a given error rate, the hamming distance between correct inputs and faulty inputs as well as the hamming distance between a correct result and a faulty result is preserved throughout processing thereby enabling correction of up to transient faults per computation cycle. The new method is compared and contrasted with current protection methods and its cost / performance is analyzed.

cs.AR↗

arXiv2011

Stabilizing data-link over non-FIFO channels with optimal fault-resilience

Self-stabilizing systems have the ability to converge to a correct behavior when started in any configuration. Most of the work done so far in the self-stabilization area assumed either communication via shared memory or via FIFO channels. This paper is the first to lay the bases for the design of self-stabilizing message passing algorithms over unreliable non-FIFO channels. We propose a fault-send-deliver optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels.

cs.DC↗

arXiv2010

Deterministic and Energy-Optimal Wireless Synchronization

We consider the problem of clock synchronization in a wireless setting where processors must power-down their radios in order to save energy. Energy efficiency is a central goal in wireless networks, especially if energy resources are severely limited. In the current setting, the problem is to synchronize clocks of $m$ processors that wake up in arbitrary time points, such that the maximum difference between wake up times is bounded by a positive integer $n$, where time intervals are appropriately discretized. Currently, the best-known results for synchronization for single-hop networks of $m$ processors is a randomized algorithm due to \cite{BKO09} of O(\sqrt {n /m} \cdot poly-log(n)) awake times per processor and a lower bound of Omega(\sqrt{n/m}) of the number of awake times needed per processor \cite{BKO09}. The main open question left in their work is to close the poly-log gap between the upper and the lower bound and to de-randomize their probabilistic construction and eliminate error probability. This is exactly what we do in this paper. That is, we show a {deterministic} algorithm with radio use of Theta(\sqrt {n /m}) that never fails. We stress that our upper bound exactly matches the lower bound proven in \cite{BKO09}, up to a small multiplicative constant. Therefore, our algorithm is {optimal} in terms of energy efficiency and completely resolves a long sequence of works in this area. In order to achieve these results we devise a novel {adaptive} technique that determines the times when devices power their radios on and off. In addition, we prove several lower bounds on the energy efficiency of algorithms for {multi-hop networks}. Specifically, we show that any algorithm for multi-hop networks must have radio use of Omega(\sqrt n) per processor.

cs.DC↗

arXiv2010

Efficient Collaborative Application Monitoring Scheme for Mobile Networks

New operating systems for mobile devices allow their users to download millions of applications created by various individual programmers, some of which may be malicious or flawed. In order to detect that an application is malicious, monitoring its operation in a real environment for a significant period of time is often required. Mobile devices have limited computation and power resources and thus are limited in their monitoring capabilities. In this paper we propose an efficient collaborative monitoring scheme that harnesses the collective resources of many mobile devices, "vaccinating" them against potentially unsafe applications. We suggest a new local information flooding algorithm called "TTL Probabilistic Propagation" (TPP). The algorithm periodically monitors one or more application and reports its conclusions to a small number of other mobile devices, who then propagate this information onwards. The algorithm is analyzed, and is shown to outperform existing state of the art information propagation algorithms, in terms of convergence time as well as network overhead. The maximal "load" of the algorithm (the fastest arrival rate of new suspicious applications, that can still guarantee complete monitoring), is analytically calculated and shown to be significantly superior compared to any non-collaborative approach. Finally, we show both analytically and experimentally using real world network data that implementing the proposed algorithm significantly reduces the number of infected mobile devices. In addition, we analytically prove that the algorithm is tolerant to several types of Byzantine attacks where some adversarial agents may generate false information, or abuse the algorithm in other ways.

cs.MA↗

arXiv2010

RoboCast: Asynchronous Communication in Robot Networks

This paper introduces the \emph{RoboCast} communication abstraction. The RoboCast allows a swarm of non oblivious, anonymous robots that are only endowed with visibility sensors and do not share a common coordinate system, to asynchronously exchange information. We propose a generic framework that covers a large class of asynchronous communication algorithms and show how our framework can be used to implement fundamental building blocks in robot networks such as gathering or stigmergy. In more details, we propose a RoboCast algorithm that allows robots to broadcast their local coordinate systems to each others. Our algorithm is further refined with a local collision avoidance scheme. Then, using the RoboCast primitive, we propose algorithms for deterministic asynchronous gathering and binary information exchange.

cs.DC↗

arXiv2010

Practically Stabilizing Atomic Memory

A self-stabilizing simulation of a single-writer multi-reader atomic register is presented. The simulation works in asynchronous message-passing systems, and allows processes to crash, as long as at least a majority of them remain working. A key element in the simulation is a new combinatorial construction of a bounded labeling scheme that can accommodate arbitrary labels, i.e., including those not generated by the scheme itself.

cs.DC↗

arXiv2010

Fast Self-Stabilizing Minimum Spanning Tree Construction

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor $Θ(n)$, to the price of increasing the best known space complexity by a factor $O(\log n)$. The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only $O(\log^2n)$ bits.

cs.DC↗