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28
Locally scalable randomized consensus for synchronous crash failures
 in Proceedings of the 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA
, 2009
"... We consider bit communication complexity of binary consensus in synchronous message passing systems with processes prone to crashes. A distributed algorithm is locally scalable when each process contributes to the complexity measure an amount that is polylogarithmic in the size n of the system, and ..."
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We consider bit communication complexity of binary consensus in synchronous message passing systems with processes prone to crashes. A distributed algorithm is locally scalable when each process contributes to the complexity measure an amount that is polylogarithmic in the size n of the system, and it is globally scalable when the average contribution per process to the complexity measure is such. We show that consensus can be solved by a randomized algorithm that is locally scalable with respect to both time and bit communication complexities against oblivious adversaries. If a bound t on the number of crashes is a constant fraction of the number n of processes then our randomized consensus solution terminates in the expected O(log n) time while the expected number of bits that each process sends and receives is O(log n). Our solution uses overlay networks with topologies that are explicitly defined and have suitable connectivity and robustness properties related to graph expansion. To compare our results to deterministic consensus solutions, it is known [20] that consensus cannot be solved deterministically by an algorithm that is locally scalable with respect to message complexity and that deterministic solutions globally scalable with respect to bit communication complexity exist for any bound t < n on the number of crashes. We prove a lower bound relating the number of nonfaulty processes needed to obtain a specific message complexity of consensus of a randomized algorithm run against oblivious adversaries.
The Contest Between Simplicity and Efficiency in Asynchronous Byzantine Agreement
"... In the wake of the decisive impossibility result of Fischer, Lynch, and Paterson for deterministic consensus protocols in the aynchronous model with just one failure, BenOr and Bracha demonstrated that the problem could be solved with randomness, even for Byzantine failures. Both protocols are natu ..."
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Cited by 3 (1 self)
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In the wake of the decisive impossibility result of Fischer, Lynch, and Paterson for deterministic consensus protocols in the aynchronous model with just one failure, BenOr and Bracha demonstrated that the problem could be solved with randomness, even for Byzantine failures. Both protocols are natural and intuitive to verify, and Bracha’s achieves optimal resilience. However, the expected running time of these protocols is exponential in general. Recently, Kapron, Kempe, King, Saia, and Sanwalani presented the first efficient Byzantine agreement algorithm in the asynchronous, full information model, running in polylogarithmic time. Their algorithm is Monte Carlo and drastically departs from the simple structure of BenOr and Bracha’s Las Vegas algorithms. In this paper, we begin an investigation of the question: to what extent is this departure necessary? Might there be a much simpler and intuitive Las Vegas protocol that runs in expected polynomial time? We will show that the exponential running time of BenOr and Bracha’s algorithms is no mere accident of their specific details, but rather an unavoidable consequence of their general symmetry and round structure. We define a natural class of “fully symmetric round protocols ” for solving Byzantine agreement in an asynchronous setting and show that any such protocol can be forced to run in expected exponential time by an adversary in the full information model. We assume the adversary controls t Byzantine processors for t = cn, where c is an arbitrary positive constant < 1 3. We view our result as a step toward identifying the level of complexity required for a polynomialtime algorithm in this setting, and also as a guide in the search for new efficient algorithms. 1
Algorithmbased fault tolerance applied to P2P computing networks
 ap2ps, 2009 First International Conference on Advances in P2P Systems 144–149
, 2009
"... Abstract—P2P computing platforms are subject to a wide range of attacks. In this paper, we propose a generalisation of the previous diskless checkpointing approach for faulttolerance in High Performance Computing systems. Our contribution is in two directions: first, instead of restricting to 2D ..."
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Abstract—P2P computing platforms are subject to a wide range of attacks. In this paper, we propose a generalisation of the previous diskless checkpointing approach for faulttolerance in High Performance Computing systems. Our contribution is in two directions: first, instead of restricting to 2D checksums that tolerate only a small number of node failures, we propose to base diskless checkpointing on linear codes to tolerate potentially a large number of faults. Then, we compare and analyse the use of Low Density Parity Check (LDPC) to classical ReedSolomon (RS) codes with respect to different fault models to fit P2P systems. Our LDPC diskless checkpointing method is well suited when only node disconnections are considered, but cannot deal with byzantine peers. Our RS diskless checkpointing method tolerates such byzantine errors, but is restricted to exact finite field computations. KeywordsABFT; P2P; distributed computing; SUMMA; linear coding; faulttolerance I.
Optimally Resilient and Adaptively Secure MultiParty Computation with Low Communication Locality
"... Secure multiparty computation (MPC) has been thoroughly studied over the past decades. The vast majority of works assume a full communication pattern: every party exchanges messages with all the network participants over a complete network of pointtopoint channels. This can be problematic in mode ..."
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Secure multiparty computation (MPC) has been thoroughly studied over the past decades. The vast majority of works assume a full communication pattern: every party exchanges messages with all the network participants over a complete network of pointtopoint channels. This can be problematic in modern large scale networks, where the number of parties can be of the order of millions, as for example when computing on large distributed data. Motivated by the above observation, Boyle, Goldwasser, and Tessaro [TCC 2013] recently put forward the notion of communication locality, namely, the total number of pointtopoint channels that each party uses in the protocol, as a quality metric of MPC protocols. They proved that assuming a publickey infrastructure (PKI) and a common reference string (CRS), an MPC protocol can be constructed for computing any nparty function, with communication locality O(log c n) and round complexity O(log c′ n), for appropriate constants c and c ′. Their protocol tolerates a static (i.e., nonadaptive) adversary corrupting up to t < ( 1 3
Author manuscript, published in "IEEE First International Conference on Advances in P2P Systems (2009)" DOI: 10.1109/AP2PS.2009.30 Algorithmbased Fault Tolerance Applied to P2P Computing Networks
, 2013
"... Abstract—P2P computing platforms are subject to a wide range of attacks. In this paper, we propose a generalisation of the previous diskless checkpointing approach for faulttolerance in High Performance Computing systems. Our contribution is in two directions: first, instead of restricting to 2D c ..."
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Abstract—P2P computing platforms are subject to a wide range of attacks. In this paper, we propose a generalisation of the previous diskless checkpointing approach for faulttolerance in High Performance Computing systems. Our contribution is in two directions: first, instead of restricting to 2D checksums that tolerate only a small number of node failures, we propose to base diskless checkpointing on linear codes to tolerate potentially a large number of faults. Then, we compare and analyse the use of Low Density Parity Check (LDPC) to classical ReedSolomon (RS) codes with respect to different fault models to fit P2P systems. Our LDPC diskless checkpointing method is well suited when only node disconnections are considered, but cannot deal with byzantine peers. Our RS diskless checkpointing method tolerates such byzantine errors, but is restricted to exact finite field computations. KeywordsABFT; P2P; distributed computing; SUMMA; linear coding; faulttolerance I.
IIICXT: Collaborative Research: Computational Methods for Understanding Social Interactions in Animal Populations
"... Which individual will animals follow when moving away from a predator? When one of the animals leaves the population, will it affect the entire social structure? Which females are likely to form a harem? Will a group of animals move together or disperse when their territory is destroyed? For animals ..."
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Which individual will animals follow when moving away from a predator? When one of the animals leaves the population, will it affect the entire social structure? Which females are likely to form a harem? Will a group of animals move together or disperse when their territory is destroyed? For animals that live in groups, social interactions and structure play a key role in their response to
Liverpool L69 3BX, U.K.
"... We study communication complexity of consensus in synchronous messagepassing systems with processes prone to crashes. The goal in the consensus problem is to have all the nonfaulty processes agree on a common value from among the input ones, after each process has been initialized with a binary inp ..."
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We study communication complexity of consensus in synchronous messagepassing systems with processes prone to crashes. The goal in the consensus problem is to have all the nonfaulty processes agree on a common value from among the input ones, after each process has been initialized with a binary input value. The system consists of n processes and it is assumed that at most t < n processes crash in an execution. A consensus algorithm that tolerates up to t failures is called fast when its time complexity is O(t). All the previously known fast deterministic consensus solutions sent Ω(n 2) bits in messages. We give a fast deterministic consensus algorithm that has processes send only O(n log 4 n) bits. In our solution, processes exchange messages according to topologies of overlay graphs that have suitable robustness and connectivity properties related to graph expansion.
University of Liverpool, U.K.
"... Abstract. We present a scalable quantum algorithm to solve binary consensus in a system of n crashprone quantum processes. The algorithm works in O(polylog n) time sending O(n polylog n) qubits against the adaptive adversary. The time performance of this algorithm is asymptotically better than a lo ..."
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Abstract. We present a scalable quantum algorithm to solve binary consensus in a system of n crashprone quantum processes. The algorithm works in O(polylog n) time sending O(n polylog n) qubits against the adaptive adversary. The time performance of this algorithm is asymptotically better than a lower bound Ω ( √ n / log n) on time of classical randomized algorithms against adaptive adversaries. Known classical randomized algorithms having each process send O(polylog n) messages work only for oblivious adversaries. Our quantum algorithm has a better time performance than deterministic solutions, which have to work in Ω(t) time for t < n failures. 1
an AFOSR MURI grant.
"... shows that it is possible to solve the Byzantine agreement, leader election and universe reduction problems in the full information model with Õ(n3/2) total bits sent. However, this result, while theoretically interesting, is not practical due to large hidden constants. In this paper, we design a ne ..."
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shows that it is possible to solve the Byzantine agreement, leader election and universe reduction problems in the full information model with Õ(n3/2) total bits sent. However, this result, while theoretically interesting, is not practical due to large hidden constants. In this paper, we design a new practical algorithm, based on this theoretical result. For networks containing more than about 1, 000 processors, our new algorithm sends significantly fewer bits than a wellknown algorithm due to Cachin, Kursawe and Shoup. To obtain our practical algorithm, we relax the fault model compared to the model of King and Saia by (1) allowing the adversary to control only a 1/8, and not a 1/3 fraction of the processors; and (2) assuming the existence of a cryptographic bit commitment primitive. Our algorithm assumes a partially synchronous communication model, where any message sent from one honest player to another honest player needs at most ∆ time steps to be received and processed by the recipient for some fixed ∆, and we assume that the clock speeds of the honest players are roughly the same. However, the clocks do not have to be synchronized (i.e., show the same time)
Branching Random Walks on Graphs
"... We study a new distributed randomized information propagation mechanism in networks that we call a branching random walk (BRW). BRW is a generalization of the wellstudied “standard ” random walk which is a fundamental primitive useful in a wide variety of network applications ranging from token man ..."
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We study a new distributed randomized information propagation mechanism in networks that we call a branching random walk (BRW). BRW is a generalization of the wellstudied “standard ” random walk which is a fundamental primitive useful in a wide variety of network applications ranging from token management and load balancing to search, routing, information propagation and gossip. BRW is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. For instance, this could be a node that has a piece of data, rumor, or a virus. In a BRW, in any step, each active node chooses k random neighbors to become active for the next step. A node is active for step t + 1 only if it is chosen by an active node in step t. This results in a branching type process in the underlying network which has interesting properties that are strikingly different from the standard random walk, which is equivalent to BRW with branching factor k = 1. Similar to the standard random walk, we focus on the cover time, which is the the number of steps for the walk to reach all the nodes and the partial cover time, which is the number of steps needed for the walk to reach at least a constant fraction of the nodes. We derive almosttight bounds on cover time and partial cover time in expander graphs, an important