# Probability Convergence in a Multithreaded Counting Application

## Abstract

We introduce the PDtree, a data structure for fast counting of any specified combinations of a given set of variables. We describe a static implementation that provides speedup linear in the number of processors on the multithreaded Cray MTA-2 machine. Finally, we prove a general convergence property that bounds the nondeterministic deviation of probability estimates relative to a sequential implementation. This convergence result is relevant for any counting application that takes a multithreaded streaming approach.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 910005

- Report Number(s):
- PNNL-SA-53295

TRN: US200723%%313

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Conference

- Resource Relation:
- Conference: Parallel and Distributed Processing Symposium (IPDPS 2007), 1-5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CONVERGENCE; PROBABILITY; P CODES; CRAY COMPUTERS; COMPUTER CALCULATIONS

### Citation Formats

```
Scherrer, Chad, Beagley, Nathaniel, Nieplocha, Jarek, Marquez, Andres, Feo, John, and Chavarría-Miranda, Daniel.
```*Probability Convergence in a Multithreaded Counting Application*. United States: N. p., 2007.
Web. doi:10.1109/IPDPS.2007.370688.

```
Scherrer, Chad, Beagley, Nathaniel, Nieplocha, Jarek, Marquez, Andres, Feo, John, & Chavarría-Miranda, Daniel.
```*Probability Convergence in a Multithreaded Counting Application*. United States. doi:10.1109/IPDPS.2007.370688.

```
Scherrer, Chad, Beagley, Nathaniel, Nieplocha, Jarek, Marquez, Andres, Feo, John, and Chavarría-Miranda, Daniel. Fri .
"Probability Convergence in a Multithreaded Counting Application". United States.
doi:10.1109/IPDPS.2007.370688.
```

```
@article{osti_910005,
```

title = {Probability Convergence in a Multithreaded Counting Application},

author = {Scherrer, Chad and Beagley, Nathaniel and Nieplocha, Jarek and Marquez, Andres and Feo, John and Chavarría-Miranda, Daniel},

abstractNote = {We introduce the PDtree, a data structure for fast counting of any specified combinations of a given set of variables. We describe a static implementation that provides speedup linear in the number of processors on the multithreaded Cray MTA-2 machine. Finally, we prove a general convergence property that bounds the nondeterministic deviation of probability estimates relative to a sequential implementation. This convergence result is relevant for any counting application that takes a multithreaded streaming approach.},

doi = {10.1109/IPDPS.2007.370688},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Mar 30 00:00:00 EDT 2007},

month = {Fri Mar 30 00:00:00 EDT 2007}

}

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