arXiv subjects

Michel Raynal

Publications and source records attributed to Michel Raynal.

52 records · Page 3Linked to original sources

arXiv2016

From Byzantine Failures to Crash Failures in Message-Passing Systems: a BG Simulation-based approach

The BG-simulation is a powerful reduction algorithm designed for asynchronous read/write crash-prone systems. It allows a set of $(t+1)$ asynchronous sequential processes to wait-free simulate (i.e., despite the crash of up to $t$ of them) an arbitrary number $n$ of processes under the assumption that at most $t$ of them may crash. The BG simulation shows that, in read/write systems, the crucial parameter is not the number $n$ of processes, but the upper bound $t$ on the number of process crashes. The paper extends the concept of BG simulation to asynchronous message-passing systems prone to Byzantine failures. Byzantine failures are the most general type of failure: a faulty process can exhibit any arbitrary behavior. Because of this, they are also the most difficult to analyze and to handle algorithmically. The main contribution of the paper is a signature-free reduction of Byzantine failures to crash failures. Assuming $t<\min(n',n/3)$, the paper presents an algorithm that simulates a system of $n'$ processes where up to $t$ may crash, on top of a basic system of $n$ processes where up to $t$ may be Byzantine. While topological techniques have been used to relate the computability of Byzantine failure-prone systems to that of crash failure-prone ones, this simulation is the first, to our knowledge, that establishes this relation directly, in an algorithmic way. In addition to extending the basic BG simulation to message-passing systems and failures more severe than process crashes, being modular and direct, this simulation provides us with a deeper insight in the nature and understanding of crash and Byzantine failures in the context of asynchronous message-passing systems. Moreover, it also allows crash-tolerant algorithms, designed for asynchronous read/write systems, to be executed on top of asynchronous message-passing systems prone to Byzantine failures.

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arXiv2016

Vertex Coloring with Communication and Local Memory Constraints in Synchronous Broadcast Networks

The vertex coloring problem has received a lot of attention in the context of synchronous round-based systems where, at each round, a process can send a message to all its neighbors, and receive a message from each of them. Hence, this communication model is particularly suited to point-to-point communication channels. Several vertex coloring algorithms suited to these systems have been proposed. They differ mainly in the number of rounds they require and the number of colors they use. This paper considers a broadcast/receive communication model in which message collisions and message conflicts can occur (a collision occurs when, during the same round, messages are sent to the same process by too many neighbors; a conflict occurs when a process and one of its neighbors broadcast during the same round). This communication model is suited to systems where processes share communication bandwidths. More precisely,the paper considers the case where, during a round, a process may either broadcast a message to its neighbors or receive a message from at most $m$ of them. This captures communication-related constraints or a local memory constraint stating that, whatever the number of neighbors of a process, its local memory allows it to receive and store at most $m$ messages during each round. The paper defines first the corresponding generic vertex multi-coloring problem (a vertex can have several colors). It focuses then on tree networks, for which it presents a lower bound on the number of colors $K$ that are necessary (namely, $K=\lceil\fracΔ{m}\rceil+1$, where $Δ$ is the maximal degree of the communication graph), and an ssociated coloring algorithm, which is optimal with respect to $K$.

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arXiv2016

Two-Bit Messages are Sufficient to Implement Atomic Read/Write Registers in Crash-prone Systems

Atomic registers are certainly the most basic objects of computing science. Their implementation on top of an n-process asynchronous message-passing system has received a lot of attention. It has been shown that t \textless{} n/2 (where t is the maximal number of processes that may crash) is a necessary and sufficient requirement to build an atomic register on top of a crash-prone asynchronous message-passing system. Considering such a context, this paper presents an algorithm which implements a single-writer multi-reader atomic register with four message types only, and where no message needs to carry control information in addition to its type. Hence, two bits are sufficient to capture all the control information carried by all the implementation messages. Moreover, the messages of two types need to carry a data value while the messages of the two other types carry no value at all. As far as we know, this algorithm is the first with such an optimality property on the size of control information carried by messages. It is also particularly efficient from a time complexity point of view.

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arXiv2016

Time-Efficient Read/Write Register in Crash-prone Asynchronous Message-Passing Systems

The atomic register is certainly the most basic object of computing science. Its implementation on top of an n-process asynchronous message-passing system has received a lot of attention. It has been shown that t \textless{} n/2 (where t is the maximal number of processes that may crash) is a necessary and sufficient requirement to build an atomic register on top of a crash-prone asynchronous message-passing system. Considering such a context, this paper visits the notion of a fast implementation of an atomic register, and presents a new time-efficient asynchronous algorithm. Its time-efficiency is measured according to two different underlying synchrony assumptions. Whatever this assumption, a write operation always costs a round-trip delay, while a read operation costs always a round-trip delay in favorable circumstances (intuitively, when it is not concurrent with a write). When designing this algorithm, the design spirit was to be as close as possible to the one of the famous ABD algorithm (proposed by Attiya, Bar-Noy, and Dolev).

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arXiv2016

Optimal Collision/Conflict-free Distance-2 Coloring in Synchronous Broadcast/Receive Tree Networks

This article is on message-passing systems where communication is (a) synchronous and (b) based on the "broadcast/receive" pair of communication operations. "Synchronous" means that time is discrete and appears as a sequence of time slots (or rounds) such that each message is received in the very same round in which it is sent. "Broadcast/receive" means that during a round a process can either broadcast a message to its neighbors or receive a message from one of them. In such a communication model, no two neighbors of the same process, nor a process and any of its neighbors, must be allowed to broadcast during the same time slot (thereby preventing message collisions in the first case, and message conflicts in the second case). From a graph theory point of view, the allocation of slots to processes is know as the distance-2 coloring problem: a color must be associated with each process (defining the time slots in which it will be allowed to broadcast) in such a way that any two processes at distance at most 2 obtain different colors, while the total number of colors is "as small as possible". The paper presents a parallel message-passing distance-2 coloring algorithm suited to trees, whose roots are dynamically defined. This algorithm, which is itself collision-free and conflict-free, uses $Δ+ 1$ colors where $Δ$ is the maximal degree of the graph (hence the algorithm is color-optimal). It does not require all processes to have different initial identities, and its time complexity is $O(d Δ)$, where d is the depth of the tree. As far as we know, this is the first distributed distance-2 coloring algorithm designed for the broadcast/receive round-based communication model, which owns all the previous properties.

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arXiv2015

A Necessary Condition for Byzantine $k$-Set Agreement

This short paper presents a necessary condition for Byzantine $k$-set agreement in (synchronous or asynchronous) message-passing systems and asynchronous shared memory systems where the processes communicate through atomic single-writer multi-reader registers. It gives a proof, which is particularly simple, that $k$-set agreement cannot be solved $t$-resiliently in an $n$-process system when $n \leq 2t + \frac{t}{k}$. This bound is tight for the case $k=1$ (Byzantine consensus) in synchronous message-passing systems.

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arXiv2015

Atomic Read/Write Memory in Signature-free Byzantine Asynchronous Message-passing Systems

This article presents a signature-free distributed algorithm which builds an atomic read/write shared memory on top of an $n$-process asynchronous message-passing system in which up to $t<n/3$ processes may commit Byzantine failures. From a conceptual point of view, this algorithm is designed to be as close as possible to the algorithm proposed by Attiya, Bar-Noy and Dolev (JACM 1995), which builds an atomic register in an $n$-process asynchronous message-passing system where up to $t<n/2$ processes may crash. The proposed algorithm is particularly simple. It does not use cryptography to cope with Byzantine processes, and is optimal from a $t$-resilience point of view ($t<n/3$). A read operation requires $O(n)$ messages, and a write operation requires $O(n^2)$ messages.

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arXiv2015

Fisheye Consistency: Keeping Data in Synch in a Georeplicated World

Over the last thirty years, numerous consistency conditions for replicated data have been proposed and implemented. Popular examples of such conditions include linearizability (or atomicity), sequential consistency, causal consistency, and eventual consistency. These consistency conditions are usually defined independently from the computing entities (nodes) that manipulate the replicated data; i.e., they do not take into account how computing entities might be linked to one another, or geographically distributed. To address this lack, as a first contribution, this paper introduces the notion of proximity graph between computing nodes. If two nodes are connected in this graph, their operations must satisfy a strong consistency condition, while the operations invoked by other nodes are allowed to satisfy a weaker condition. The second contribution is the use of such a graph to provide a generic approach to the hybridization of data consistency conditions into the same system. We illustrate this approach on sequential consistency and causal consistency, and present a model in which all data operations are causally consistent, while operations by neighboring processes in the proximity graph are sequentially consistent. The third contribution of the paper is the design and the proof of a distributed algorithm based on this proximity graph, which combines sequential consistency and causal consistency (the resulting condition is called fisheye consistency). In doing so the paper not only extends the domain of consistency conditions, but provides a generic provably correct solution of direct relevance to modern georeplicated systems.

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arXiv2015

Anonymous Obstruction-free $(n,k)$-Set Agreement with $n-k+1$ Atomic Read/Write Registers

The $k$-set agreement problem is a generalization of the consensus problem. Namely, assuming each process proposes a value, each non-faulty process has to decide a value such that each decided value was proposed, and no more than $k$ different values are decided. This is a hard problem in the sense that it cannot be solved in asynchronous systems as soon as $k$ or more processes may crash. One way to circumvent this impossibility consists in weakening its termination property, requiring that a process terminates (decides) only if it executes alone during a long enough period. This is the well-known obstruction-freedom progress condition. Considering a system of $n$ {\it anonymous asynchronous} processes, which communicate through atomic {\it read/write registers only}, and where {\it any number of processes may crash}, this paper addresses and solves the challenging open problem of designing an obstruction-free $k$-set agreement algorithm with $(n-k+1)$ atomic registers only. From a shared memory cost point of view, this algorithm is the best algorithm known so far, thereby establishing a new upper bound on the number of registers needed to solve the problem (its gain is $(n-k)$ with respect to the previous upper bound). The algorithm is then extended to address the repeated version of $(n,k)$-set agreement. As it is optimal in the number of atomic read/write registers, this algorithm closes the gap on previously established lower/upper bounds for both the anonymous and non-anonymous versions of the repeated $(n,k)$-set agreement problem. Finally, for $1 \leq x\leq k \textless{} n$, a generalization suited to $x$-obstruction-freedom is also described, which requires $(n-k+x)$ atomic registers only.

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arXiv2015

Specifying Concurrent Problems: Beyond Linearizability

Tasks and objects are two predominant ways of specifying distributed problems. A task is specified by an input/output relation, defining for each set of processes that may run concurrently, and each assignment of inputs to the processes in the set, the valid outputs of the processes. An object is specified by an automaton describing the outputs the object may produce when it is accessed sequentially. Thus, tasks explicitly state what may happen only when sets of processes run concurrently, while objects only specify what happens when processes access the object sequentially. Each one requires its own implementation notion, to tell when an execution satisfies the specification. For objects linearizability is commonly used, a very elegant and useful consistency condition. For tasks implementation notions are less explored. The paper introduces the notion of interval-sequential object. The corresponding implementation notion of interval-linearizability generalizes linearizability, and allows to associate states along the interval of execution of an operation. Interval-linearizability allows to specify any task, however, there are sequential one-shot objects that cannot be expressed as tasks, under the simplest interpretation of a task. It also shows that a natural extension of the notion of a task is expressive enough to specify any interval-sequential object.

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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.

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arXiv2011

Failure Detectors in Homonymous Distributed Systems (with an Application to Consensus)

This paper addresses the consensus problem in homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership ("homonymous" means that several processes may have the same identifier). New classes of failure detectors suited to these systems are first defined. Among them, the classes HΩ and HΣ are introduced that are the homonymous counterparts of the classes Ω and Σ, respectively. (Recall that the pair <Ω,Σ> defines the weakest failure detector to solve consensus.) Then, the paper shows how HΩ and HΣ can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge of the membership. One algorithm solves consensus with , while the other uses only HΩ, but needs a majority of correct processes. Observe that the systems with unique identifiers and anonymous systems are extreme cases of homonymous systems from which follows that all these results also apply to these systems. Interestingly, the new failure detector class HΩ can be implemented with partial synchrony, while the analogous class AΩ defined for anonymous systems can not be implemented (even in synchronous systems). Hence, the paper provides us with the first proof showing that consensus can be solved in anonymous systems with only partial synchrony (and a majority of correct processes).

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arXiv2008

Timed Quorum System for Large-Scale and Dynamic Environments

This paper presents Timed Quorum System (TQS), a new quorum system especially suited for large-scale and dynamic systems. TQS requires that two quorums intersect with high probability if they are used in the same small period of time. It proposed an algorithm that implements TQS and that verifies probabilistic atomicity: a consistency criterion that requires each operation to respect atomicity with high probability. This TQS implementation has quorum of size O(\sqrt{nD}) and expected access time of O(log \sqrt{nD}) message delays, where n measures the size of the system and D is a required parameter to handle dynamism.

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arXiv2008

Core Persistence in Peer-to-Peer Systems: Relating Size to Lifetime

Distributed systems are now both very large and highly dynamic. Peer to peer overlay networks have been proved efficient to cope with this new deal that traditional approaches can no longer accommodate. While the challenge of organizing peers in an overlay network has generated a lot of interest leading to a large number of solutions, maintaining critical data in such a network remains an open issue. In this paper, we are interested in defining the portion of nodes and frequency one has to probe, given the churn observed in the system, in order to achieve a given probability of maintaining the persistence of some critical data. More specifically, we provide a clear result relating the size and the frequency of the probing set along with its proof as well as an analysis of the way of leveraging such an information in a large scale dynamic distributed system.

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arXiv2007

Distributed Slicing in Dynamic Systems

Peer to peer (P2P) systems are moving from application specific architectures to a generic service oriented design philosophy. This raises interesting problems in connection with providing useful P2P middleware services capable of dealing with resource assignment and management in a large-scale, heterogeneous and unreliable environment. The slicing service, has been proposed to allow for an automatic partitioning of P2P networks into groups (slices) that represent a controllable amount of some resource and that are also relatively homogeneous with respect to that resource. In this paper we propose two gossip-based algorithms to solve the distributed slicing problem. The first algorithm speeds up an existing algorithm sorting a set of uniform random numbers. The second algorithm statistically approximates the rank of nodes in the ordering. The scalability, efficiency and resilience to dynamics of both algorithms rely on their gossip-based models. These algorithms are proved viable theoretically and experimentally.

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arXiv2006

Distributed Slicing in Dynamic Systems

Peer to peer (P2P) systems are moving from application specific architectures to a generic service oriented design philosophy. This raises interesting problems in connection with providing useful P2P middleware services that are capable of dealing with resource assignment and management in a large-scale, heterogeneous and unreliable environment. One such service, the slicing service, has been proposed to allow for an automatic partitioning of P2P networks into groups (slices) that represent a controllable amount of some resource and that are also relatively homogeneous with respect to that resource, in the face of churn and other failures. In this report we propose two algorithms to solve the distributed slicing problem. The first algorithm improves upon an existing algorithm that is based on gossip-based sorting of a set of uniform random numbers. We speed up convergence via a heuristic for gossip peer selection. The second algorithm is based on a different approach: statistical approximation of the rank of nodes in the ordering. The scalability, efficiency and resilience to dynamics of both algorithms relies on their gossip-based models. We present theoretical and experimental results to prove the viability of these algorithms.

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