Kronecker descriptor partitioning for parallel algorithms

Czekster, Ricardo M.; Rose, César A. F. De; Fernandes, Paulo; Lima, Antonio M.; Webber, Thais

doi:10.1145/1878537.1878789

Cited by 6 publications

(4 citation statements)

References 6 publications

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“…Recent developments include the Slice [16] and Split [14] algorithms for vector-descriptor products, which allow parallel implementation while retaining the beneficial properties of the Shuffle algorithm.…”

Section: Definitionmentioning

confidence: 99%

Efficient Decomposition Algorithm for Stationary Analysis of Complex Stochastic Petri Net Models

Marussy

Klenik

Molnár³

et al. 2016

Application and Theory of Petri Nets and Concurrency

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Abstract. Stochastic Petri nets are widely used for the modeling and analysis of non-functional properties of critical systems. The state space explosion problem often inhibits the numerical analysis of such models. Symbolic techniques exist to explore the discrete behavior of even complex models, while block Kronecker decomposition provides memoryefficient representation of the stochastic behavior. However, the combination of these techniques into a stochastic analysis approach is not straightforward. In this paper we integrate saturation-based symbolic techniques and decomposition-based stochastic analysis methods. Saturation-based exploration is used to build the state space representation and a new algorithm is introduced to efficiently build block Kronecker matrix representation to be used by the stochastic analysis algorithms. Measurements confirm that the presented combination of the two representations can expand the limits of previous approaches.

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Section: Definitionmentioning

confidence: 99%

Efficient Decomposition Algorithm for Stationary Analysis of Complex Stochastic Petri Net Models

Marussy

Klenik

Molnár³

et al. 2016

Application and Theory of Petri Nets and Concurrency

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“…Recent developments include the SPLIT [16] algorithm, which allows parallel implementation while retaining the beneficial properties of the SHUFFLE algorithm. Implementation of SPLIT and the development of heuristics for its acceleration are in the scope of our ongoing work.…”

Section: The Individual Blocks Are Sums Of Kronecker Productsmentioning

confidence: 99%

Configurable numerical analysis for stochastic systems

Marussy

Klenik

Molnár³

et al. 2016

2016 International Workshop on Symbolic and Numerical Methods for Reachability Analysis (SNR)

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Abstract-Stochastic aspects of complex systems require more and more involved analysis approaches. Answering reachability and related analysis questions can often be reduced to steadystate, transient, reward or sensitivity value analysis of stochastic models. In this paper we introduce a configurable stochastic analysis framework which supports the user to combine explicit, symbolic and numerical algorithms to efficiently compute the measures of stochastic models. Beyond the well-known algorithms from the field, we also developed an experimental version of an Induced Dimensionality Reduction Stabilized numerical solver to compute steady-state probabilities of Markovian models. As far as we know, this is the first attempt to exploit this algorithm in stochastic analysis. We have conducted experiments on different combinations of the algorithms on various models to assess their advantages and disadvantages in the analysis. This information can be used by the user to choose the combination of algorithms being efficient solving the analysis problem.

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“…Therefore, as most of the current machines are based on multi-core technology, the development of parallel solutions to accelerate VDP operations becomes essential. Czekster et al [13] have developed a parallel solution of Kronecker Descriptors considering data partitioning strategies for the Split algorithm. However, this first parallel approach was only based on MPI [26] primitives and presented low scalability on a distributed memory computing platform.…”

Section: Introductionmentioning

confidence: 99%