Learning Sequential and Parallel Runtime Distributions for Randomized Algorithms

Arbeláez, Alejandro; Truchet, Charlotte; O’Sullivan, Barry

doi:10.1109/ictai.2016.0105

Cited by 4 publications

(6 citation statements)

References 32 publications

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“…For instance, for many algorithms, the distribution for a certain class of problems has been observed empirically. Arbelaez et al [2] use a machine learning approach to predict the runtime distributions of several randomized algorithms. This knowledge can be used to obtain a better restart strategy for this class of problems.…”

Section: Introductionmentioning

confidence: 99%

Runtime Distributions and Criteria for Restarts

Lorenz

2017

SOFSEM 2018: Theory and Practice of Computer Science

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Randomized algorithms sometimes employ a restart strategy. After a certain number of steps, the current computation is aborted and restarted with a new, independent random seed. In some cases, this results in an improved overall expected runtime. This work introduces properties of the underlying runtime distribution which determine whether restarts are advantageous. The most commonly used probability distributions admit the use of a scale and a location parameter. Location parameters shift the density function to the right, while scale parameters affect the spread of the distribution. It is shown that for all distributions scale parameters do not influence the usefulness of restarts and that location parameters only have a limited influence. This result simplifies the analysis of the usefulness of restarts. The most important runtime probability distributions are the log-normal, the Weibull, and the Pareto distribution. In this work, these distributions are analyzed for the usefulness of restarts. Secondly, a condition for the optimal restart time (if it exists) is provided. The log-normal, the Weibull, and the generalized Pareto distribution are analyzed in this respect. Moreover, it is shown that the optimal restart time is also not influenced by scale parameters and that the influence of location parameters is only linear.

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Section: Introductionmentioning

confidence: 99%

Runtime Distributions and Criteria for Restarts

Lorenz

2017

SOFSEM 2018: Theory and Practice of Computer Science

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“…The lognormal, the Weibull and the GP distribution were already considered as suitable in previous research articles. Most notably Arbelaez et al [3] observed that the runtime behavior of randomly generated 3-SAT instances with a clause to variable ratio of 4.2 can be described by lognormal distributions. Other results favoring the lognormal distribution are given by Arbelaez et al [2] and Truchet et al [22].…”

Section: Runtime Distributionsmentioning

confidence: 99%

“…The SATzilla feature extractor by Xu et al [25] creates the features of the instances (as motivated by Arbelaez et al [3]). It is called with the parameters -base, -ls and -lobjois, leading to a total of 81 features.…”

Section: Feature Extractionmentioning

confidence: 99%

“…This is called the (empirical) runtime distribution. Arbelaez et al [3] studied the empirical runtime distribution of probSAT, a stochastic local search SAT-solver by Balint and Schöning [5], and found that lognormal distributions describe the runtime behavior well. A recent development in the field is trying to predict the runtime distributions of unseen instances with machine learning methods (see for example Arbelaez et al [3], Eggensperger et al [9]).…”

Section: Introductionmentioning

confidence: 99%

“…Our contribution: This work analyzes the capability of probability distributions to describe the runtime behavior of probSAT on random 3-SAT instances close to the phase transition. We approximate the runtime distributions of prob-SAT with a similar methodology as presented by Arbelaez et al [3]. In our work, the generalized Pareto, the lognormal and the Weibull distribution are used to describe the runtime behavior.…”

Section: Introductionmentioning

confidence: 99%

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The Potential of Restarts for ProbSAT

Lorenz

Nickerl

2020

Computer Aided Systems Theory – EUROCAST 2019

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This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT [4,5], by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.

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On the Complexity of Restarting

Lorenz

2019

Computer Science – Theory and Applications

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Learning Sequential and Parallel Runtime Distributions for Randomized Algorithms

Cited by 4 publications

References 32 publications

Runtime Distributions and Criteria for Restarts

Runtime Distributions and Criteria for Restarts

The Potential of Restarts for ProbSAT

On the Complexity of Restarting

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