Deciding 1-solvability of distributed task is NP-hard

Biran, Ofer; Moran, Shlomo; Zaks, Shmuel

doi:10.1007/3-540-53832-1_44

Cited by 7 publications

(7 citation statements)

References 7 publications

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“…Then Biran, Moran and Zaks proved that there is a 1-resilient message-passing algorithm to solve the task. In later papers, they also showed that determining whether a task has these properties is NP-hard for more than two processes [62], and gave very precise bounds on the round complexity of solving any task that satisfies them [63].…”

Section: Characterizing Solvable Tasksmentioning

confidence: 99%

Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

123

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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing. There is a strong emphasis in our presentation on explaining the wide variety of techniques that are used to obtain the results described.

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Section: Characterizing Solvable Tasksmentioning

confidence: 99%

Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

123

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“…We demonstrate this by extending some known impossibility results to their extremes. In a subsequent paper [BMZ1] we use this characterization to show that the problem of deciding whether a given distributed task is 1-solvable is NP-hard.…”

Section: Introductionmentioning

confidence: 99%

A combinatorial characterization of the distributed 1-solvable tasks

Biran

Moran

Zaks

1990

Journal of Algorithms

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Fischer, Lynch and Paterson showed in a fundamental paper that achieving a distributed agreement is impossible in the presence of one faulty processor. This result was later extended by Moran and Wolfstahl who showed that it holds for any task with a connected input graph and a disconnected decision graph.In this paper we extend that latter result, and in fact we set an exact borderline between solvable and unsolvable tasks, by giving a necessary and sufficient condition for a task to be 1-solvable (that is: solvable in the presence of one faulty processor). Our characterization is purely combinatorial, and involves only relations between the input graph and the output graph, defined by the given task. It provides easy proofs for the non-solvability of tasks, and also provides a universal protocol which solves any task which is found to be solvable by our condition.Using the above characterization, we also derive a novel technique to prove lower bounds on the number of messages that must be sent due to processor failure; specifically, we provide a simple proof that for each fixed N > 2 there exist distributed tasks for N processors, that can be solved in the presence of a faulty processor, but any protocol that solves them must send arbitrarily many messages in the worst case.

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“…) case (wi = ) then return(wi) (7) (wi = ) then repeat Xi ← collect(W ); (8) if (∃ j : Xi[j] = ⊥, ) then return(Xi[j]) endif (9) until (⊥ / ∈ Xi) endrepeat; (10) [a1, . .…”

Section: Traversing a Labeled Binary Treementioning

confidence: 99%

“…From this point of view, our paper is a complexity study of the class of safe tasks with a particular kind of output vectors: all decisions in an execution are equal. In general, the study of f -fault tolerant decision tasks requires higher dimensional topology (except for the case of f = 1 which uses only graphs [9]), and leads to undecidable characterizations [16,17] (NP-Hard for f = 1 [10]). Due to the simplicity of the allowed output vectors, we are able to derive our results using only graph connectivity.…”

Section: Introductionmentioning

confidence: 99%

Condition-based consensus solvability: a hierarchy of conditions and efficient protocols

Mostéfaoui

Rajsbaum²,

Raynal

et al. 2004

Distributed Computing

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The condition-based approach for consensus solvability consists of identifying sets of input vectors, called conditions, for which there exists an asynchronous protocol solving consensus despite the occurrence of up to f process crashes. This paper investigates C f , the largest set of conditions which allow us to solve the consensus problem in an asynchronous shared memory system.The first part of the paper shows that C f is made up of a hierarchy of classes of conditions, CWe prove that each one is strictly contained in the previous one: CVarious properties of the hierarchy are also derived. It is shown that a class can be characterized in two equivalent but complementary ways: one is convenient for designing protocols while the other is for analyzing the class properties. The paper also defines a linear family of conditions that can be used to derive many specific conditions. In particular, for each d, two natural conditions are presented.The second part of the paper is devoted to the design of efficient condition-based protocols. A generic conditionbased protocol is presented. This protocol can be instantiated with any condition C, C ∈ C [d] f , and requires at most (2n+1) log 2 ( (f − d)/2 + 1) shared memory read/write operations per process in the synchronization part of the protocol. Thus, the value (f − d) represents the "difficulty" of the class C [d] f . An improvement of the protocol for the conditions in C[0] f is also presented.

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Deciding 1-solvability of distributed task is NP-hard

Cited by 7 publications

References 7 publications

Hundreds of impossibility results for distributed computing

Hundreds of impossibility results for distributed computing

A combinatorial characterization of the distributed 1-solvable tasks

Condition-based consensus solvability: a hierarchy of conditions and efficient protocols

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