Reachability analysis on distributed executions

Diehl, Claire; Jard, Claude; Rampon, Jean-Xavier

doi:10.1007/3-540-56610-4_94

Cited by 19 publications

(19 citation statements)

References 12 publications

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“…The following analysis shows that a minimum-sized fixed set should be used. The set CGS (c↓F ) can be built with worst-case time complexity O(|F | · |CGS (c↓F )| + |F | 3 S 2 ) using the algorithm in [DJR93], or slightly faster using the algorithm in [JMN95]. For each state g 1 in CGS (c↓F ), Garg and Waldecker's algorithm detects c↓F |= Poss Φ g1 with worst-case time complexity O(|F | 2 S).…”

Section: Lemma 1 For All Computations C All F ⊆ [1n ] and All Glmentioning

confidence: 99%

“…The algorithms in [DJR93,JMN95] for computing CGS (c) have on-line versions with the same time complexities as given above. The same is true of Garg and Waldecker's algorithm.…”

Section: On-line Algorithmmentioning

confidence: 99%

“…Any detection algorithm that constructs the entire latticewhether it uses the method in [CM91,MN91] or the more efficient schemes in [DJR93,JMN95]-has worst-case time complexity that is at least linear in the size of the lattice. Thus, Cooper and Marzullo's algorithms for detecting Poss Φ and Def Φ have worst-case time complexity Ω(S N ).…”

Section: Introductionmentioning

confidence: 99%

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Faster possibility detection by combining two approaches

Stoller

Schneider

1995

Distributed Algorithms

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Abstract.A new algorithm is presented for detecting whether a particular computation of an asynchronous distributed system satisfies Poss Φ (read "possibly Φ"), meaning the system could have passed through a global state satisfying Φ. Like the algorithm of Cooper and Marzullo, Φ may be any global state predicate; and like the algorithm of Garg and Waldecker, Poss Φ is detected quite efficiently if Φ has a certain structure. The new algorithm exploits the structure of some predicates Φ not handled by Garg and Waldecker's algorithm to detect Poss Φ more efficiently than is possible with any algorithm that, like Cooper and Marzullo's, evaluates Φ on every global state through which the system could have passed. A second algorithm is also presented for off-line detection of Poss Φ. It uses Strassen's scheme for fast matrix multiplication. The intrinsic complexity of off-line and on-line detection of Poss Φ is discussed.

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Section: Lemma 1 For All Computations C All F ⊆ [1n ] and All Glmentioning

confidence: 99%

“…The algorithms in [DJR93,JMN95] for computing CGS (c) have on-line versions with the same time complexities as given above. The same is true of Garg and Waldecker's algorithm.…”

Section: On-line Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Faster possibility detection by combining two approaches

Stoller

Schneider

1995

Distributed Algorithms

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“…This environment provides a mechanism of vectorial clocks [15], that are traced "on line". These traces are used as input for our algorithm of construction of the antichain lattice of an order [7,13]. When given as input a linear extension of 02ke-t, this algorithm has a time complexity of…”

Section: Routine Application Of Lemmas 8(1) and 5 []mentioning

confidence: 99%

Measuring concurrency of regular distributed computations

Bareau

Caillaud

Jard

et al. 1995

TAPSOFT '95: Theory and Practice of Software Development

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Abstract. In this paper we present a concurrency measure that is especially adapted to distributed programs that exhibit regular run-time behaviours, including many programs that are obtained by automatic parallelization of sequential code. This measure is based on the antichain lattice of the partial order that models the distributed execution under consideration. We show the conditions under which the measure is computable on an infinite execution that is the repetition of a finite pattern. There, the measure can be computed by considering only a bounded number of patterns, the bound being at most the number of processors. IntroductionThe trend towards the use of distributed memory parallel machines is very evident. However, their programming environments have to be significantly improved, especially in the field we are mainly interested in: semi-automated distribution of sequential code for scientific computing. Indeed, programmers need sophisticated performance evaluation tools. However, there is no well-accepted "complexity" criterion for distributed programs, for the behaviours of asynchronous message-passing programs are not yet sufficiently understood. It is also very difficult to design tools that can give relevant performance information from static analysis of distributed code. A research axis is to study runs of a distributed program instead of the program itself. Especially, it needs to define concurrency measures, i.e. measures that can help reveal the synchronization structure of a computation, as opposed to the traditional ones (message count, for instance) which only give quantitative information about the computation. For this it is now usual to take a distributed execution as a partially ordered set of events that are causally related by process sequentiMity and interprocess communication [14]. As far as we know, the first concurrency measure that takes account of causality was proposed by Charron-Bost [5], followed by [9,11,16].It is shown in [11] that either these measures are too inaccurate or their computational complexity makes them impracticable. It is also important to observe

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“…Enumeration problems have received much interest over the past decades due to their applications in computer science [1,9,15,16,25]. For these problems the size of the output may be exponential in the size of the input, which in general is different from optimisation or counting problems where the size of the output is polynomially related to the size of the input.…”

Section: Introductionmentioning

confidence: 99%

On the Enumeration of Minimal Dominating Sets and Related Notions

Kanté¹,

Limouzy²,

Mary³

et al. 2014

SIAM J. Discrete Math.

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Abstract. A dominating set D in a graph is a subset of its vertex set such that each vertex is either in D or has a neighbour in D. In this paper, we are interested in the enumeration of (inclusion-wise) minimal dominating sets in graphs, called the Dom-Enum problem. It is well known that this problem can be polynomially reduced to the Trans-Enum problem in hypergraphs, i.e., the problem of enumerating all minimal transversals in a hypergraph. Firstly we show that the Trans-Enum problem can be polynomially reduced to the Dom-Enum problem. As a consequence there exists an output-polynomial time algorithm for the Trans-Enum problem if and only if there exists one for the Dom-Enum problem. Secondly, we study the Dom-Enum problem in some graph classes. We give an output-polynomial time algorithm for the Dom-Enum problem in split graphs, and introduce the completion of a graph to obtain an output-polynomial time algorithm for the Dom-Enum problem in P 6 -free chordal graphs, a proper superclass of split graphs. Finally, we investigate the complexity of the enumeration of (inclusion-wise) minimal connected dominating sets and minimal total dominating sets of graphs. We show that there exists an output-polynomial time algorithm for the Dom-Enum problem (or equivalently Trans-Enum problem) if and only if there exists one for the following enumeration problems: minimal total dominating sets, minimal total dominating sets in split graphs, minimal connected dominating sets in split graphs, minimal dominating sets in co-bipartite graphs.

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Reachability analysis on distributed executions

Cited by 19 publications

References 12 publications

Faster possibility detection by combining two approaches

Faster possibility detection by combining two approaches

Measuring concurrency of regular distributed computations

On the Enumeration of Minimal Dominating Sets and Related Notions

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