Results 1  10
of
25
The weakest failure detector for message passing setagreement
 In DISC
, 2008
"... Abstract. In the setagreement problem, n processes seek to agree on at most n−1 different values. This paper determines the weakest failure detector to solve this problem in a messagepassing system where processes may fail by crashing. This failure detector, called the Loneliness detector and deno ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
(Show Context)
Abstract. In the setagreement problem, n processes seek to agree on at most n−1 different values. This paper determines the weakest failure detector to solve this problem in a messagepassing system where processes may fail by crashing. This failure detector, called the Loneliness detector and denoted L, outputs one of two values, “true ” or “false ” such that: (1) there is at least one process where L outputs always “false”, and(2) if only one process is correct, L eventually outputs “true ” at this process.
On the Weakest Failure Detector Ever
 PODC'07
, 2007
"... Many problems in distributed computing are impossible when no information about process failures is available. It is common to ask what information about failures is necessary and sufficient to circumvent some specific impossibility, e.g., consensus, atomic commit, mutual exclusion, etc. This paper ..."
Abstract

Cited by 14 (4 self)
 Add to MetaCart
(Show Context)
Many problems in distributed computing are impossible when no information about process failures is available. It is common to ask what information about failures is necessary and sufficient to circumvent some specific impossibility, e.g., consensus, atomic commit, mutual exclusion, etc. This paper asks what information about failures is needed to circumvent any impossibility and sufficient to circumvent some impossibility. In other words, what is the minimal yet nontrivial failure information. We present an abstraction, denoted Υ, that provides very little failure information. In every run of the distributed system, Υ eventually informs the processes that some set of processes in the system cannot be the set of correct processes in that run. Although seemingly weak, for it might provide random information for an arbitrarily long period
Looking for the Weakest Failure Detector for kSet Agreement in Messagepassing Systems
 Is Πk the End of the Road?, INRIA, 2009, http://hal.inria.fr/inria00384993/en/, PI
, 1929
"... Abstract: In the kset agreement problem, each process (in a set of n processes) proposes a value and has to decide a proposed value in such a way that at most k different values are decided. While this problem can easily be solved in asynchronous systems prone to t process crashes when k> t, it ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
Abstract: In the kset agreement problem, each process (in a set of n processes) proposes a value and has to decide a proposed value in such a way that at most k different values are decided. While this problem can easily be solved in asynchronous systems prone to t process crashes when k> t, it cannot be solved when k ≤ t. Since several years, the failure detectorbased approach has been investigated to circumvent this impossibility. While the weakest failure detector class to solve the kset agreement problem in read/write sharedmemory systems has recently been discovered (PODC 2009), the situation is different in messagepassing systems where the weakest failure detector classes are known only for the extreme cases k = 1 (consensus) and k = n − 1 (set agreement). This paper introduces a candidate for the general case. It presents a new failure detector class, denoted Πk, and shows Π1 = Σ × Ω (the weakest class for k = 1), and Πn−1 = L (the weakest class for k = n − 1). Then, the paper investigates the structure of Πk and shows it is the combination of two failures detector classes denoted Σk and Ωk (that generalize the previous “quorums ” and “eventual leaders ” failure detectors classes). Finally, the paper proves that Σk is a necessary requirement (as far as information on failure is concerned) to solve the kset agreement problem in messagepassing systems. The paper presents also a Πn−1based algorithm that solves the (n − 1)set agreement problem. This algorithm provides us with a new algorithmic insight on the way the (n − 1)set agreeement problem can be solved in asynchronous messagepassing systems (insight from the point of view of the nonpartitioning constraint defined by Σn−1).
The Iterated Restricted Immediate Snapshot Model
, 2008
"... In the Iterated Immediate Snapshot model (IIS) the memory consists of a sequence of oneshot Immediate Snapshot (IS) objects. Processes access the sequence of IS objects, onebyone, asynchronously, in a waitfree manner; any number of processes can crash. Its interest lies in the elegant recursive ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
In the Iterated Immediate Snapshot model (IIS) the memory consists of a sequence of oneshot Immediate Snapshot (IS) objects. Processes access the sequence of IS objects, onebyone, asynchronously, in a waitfree manner; any number of processes can crash. Its interest lies in the elegant recursive structure of its runs, hence of the ease to analyze it round by round. In a very interesting way, Borowsky and Gafni have shown that the IIS model and the read/write model are equivalent for the waitfree solvability of decision tasks. This paper extends the benefits of the IIS model to partially synchronous systems. Given a shared memory model enriched with a failure detector, what is an equivalent IIS model? The paper shows that an elegant way of capturing the power of a failure detector and other partially synchronous systems in the IIS model is by restricting appropriately its set of runs, giving rise to the Iterated Restricted Immediate Snapshot model (IRIS).
The Disagreement Power of an Adversary
"... Abstract. At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the p ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
(Show Context)
Abstract. At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the processes from agreeing on t values. But what about the remaining (2 2n − n) adversaries that might crash certain combination of processes and not others? This paper presents a precise way to characterize such adversaries by introducing the notion of disagreement power: the biggest integer k for which the adversary can prevent processes from agreeing on k values. We show how to compute the disagreement power of an adversary and how this notion enables to derive n equivalence classes of adversaries. 1
On set consensus numbers
 In DISC
, 2009
"... Abstract. It is conjectured that the only way a failure detector (FD) can help solving nprocess tasks is by providing kset consensus for some k ∈ {1,..., n} among all the processes. It was recently shown by Zieliński that any FD that allows for solving a given nprocess task that is unsolvable re ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
(Show Context)
Abstract. It is conjectured that the only way a failure detector (FD) can help solving nprocess tasks is by providing kset consensus for some k ∈ {1,..., n} among all the processes. It was recently shown by Zieliński that any FD that allows for solving a given nprocess task that is unsolvable readwrite waitfree, also solves (n − 1)set consensus. In this paper, we provide a generalization of Zieliński’s result. We show that any FD that solves a colorless task that cannot be solved readwrite kresiliently, also solves kset consensus. More generally, we show that every colorless task T can be characterized by its set consensus number: the largest k ∈ {1,..., n} such that T is solvable (k − 1)resiliently. A task T with set consensus number k is, in the failure detector sense, equivalent to kset consensus, i.e., a FD solves T if and only if it solves kset consensus. As a corollary, we determine the weakest FD for solving kset consensus in every environment, i.e., for all assumptions on when and where failures might occur. 1
Failure Detectors to Solve Asynchronous kSet Agreement: a Glimpse of Recent Results
"... Abstract: In the kset agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
Abstract: In the kset agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process crashes when t < k. In contrast, it has been shown that kset agreement cannot be solved in asynchronous systems when k ≤ t. Hence, since several years, the failure detectorbased approach has been investigated to circumvent this impossibility. This approach consists in enriching the underlying asynchronous system with an additional module per process that provides it with information on failures. Hence, without becoming synchronous, the enriched system is no longer fully asynchronous. This paper surveys this approach in both asynchronous shared memory systems and asynchronous message passing systems. It presents and discusses recent results and associated kset agreement algorithms.
Sharing is harder than agreeing
 IN: PODC 2008: PROCEEDINGS OF THE TWENTYSEVENTH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 2008
"... One of the most celebrated results of the theory of distributed computing is the impossibility, in an asynchronous system of n processes that communicate through shared memory registers, to solve the set agreement problem where the processes need to decide on up to n − 1 among their n initial values ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
One of the most celebrated results of the theory of distributed computing is the impossibility, in an asynchronous system of n processes that communicate through shared memory registers, to solve the set agreement problem where the processes need to decide on up to n − 1 among their n initial values. In short, the result indicates that the register abstraction is too weak to implement the set agreement one. This paper explores the relation between these abstractions in a message passing system where a register is not a given physical device but is rather itself implemented by processes communicating through message passing. We show that, maybe surprisingly, the information about process failures that is necessary and sufficient to implement a register shared by two particular processes is sufficient but not necessary to implement set agreement. We later generalize this result by considering kset agreement, where the processes can decide on up to k values, and comparing it with a register shared by any particular subset of 2k processes. We prove that, for 1 ≤ k ≤ n/2, (a) any failure information that is sufficient to implement a register shared by 2k processes is sufficient to implement (n − k)set agreement but (b) a failure information that is sufficient for (n − k)set agreement is not sufficient for a register shared by 2k processes. We also prove that (c) a failure information that is sufficient for a register shared by 2k processes is not sufficient for ((nk)1)set agreement.
Partial synchrony based on set timeliness
, 2009
"... We introduce a new model of partial synchrony for readwrite shared memory systems. This model is based on the notion of set timeliness—a natural and straightforward generalization of the seminal concept of timeliness in the partially synchrony model of Dwork, Lynch and Stockmeyer [11]. Despite its ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We introduce a new model of partial synchrony for readwrite shared memory systems. This model is based on the notion of set timeliness—a natural and straightforward generalization of the seminal concept of timeliness in the partially synchrony model of Dwork, Lynch and Stockmeyer [11]. Despite its simplicity, the concept of set timeliness is powerful enough to define a family of partially synchronous systems that closely match individual instances of the tresilient kset agreement problem among n processes, henceforth denoted (t, k, n)agreement. In particular, we use it to give a partially synchronous system that is is synchronous enough for solving (t, k, n)agreement, but not enough for solving two incrementally stronger problems, namely, (t + 1, k, n)agreement, which has a slightly stronger resiliency requirement, and (t, k − 1, n)agreement, which has a slightly stronger agreement requirement. This is the first partially synchronous system that separates between these subconsensus problems. The above results show that set timeliness can be used to study and compare the partial synchrony requirements of problems that are strictly weaker than consensus.
Algorithms for Extracting Timeliness Graphs
 Lecture Notes in Computer Science
"... We consider asynchronous messagepassing systems in which some links are timely and processes may crash. Each run defines a timeliness graph among correct processes: (p, q) is an edge of the timeliness graph if the link from p to q is timely (that is, there is bound on communication delays from p t ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
We consider asynchronous messagepassing systems in which some links are timely and processes may crash. Each run defines a timeliness graph among correct processes: (p, q) is an edge of the timeliness graph if the link from p to q is timely (that is, there is bound on communication delays from p to q). The main goal of this paper is to approximate this timeliness graph by graphs having some properties (such as being trees, rings,...). Given a family S of graphs, for runs such that the timeliness graph contains at least one graph in S then using an extraction algorithm, each correct process has to converge to the same graph in S that is, in a precise sense, an approximation of the timeliness graph of the run. For example, if the timeliness graph contains a ring, then using an extraction algorithm, all correct processes eventually converge to the same ring and in this ring all nodes will be correct processes and all links will be timely. We first present a general extraction algorithm and then a more specific extraction algorithm that is communication efficient (i.e., eventually all the messages of the extraction algorithm use only links of the extracted graph). 1