# Parallel consistent labeling algorithms

## Abstract

Mackworth and Freuder have analyzed the time complexity of several constraint satisfaction algorithms. Mohr and Henderson have given new algorithms, AC-4 and PC-3, for arc and path consistency, respectively, and have shown that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms. In this paper, they give parallel algorithms for solving node and arc consistency. They show that any parallel algorithm for enforcing arc consistency in the worst case must have O(na) sequential steps, where n is number of nodes, and a is the number of labels per node. They give several parallel algorithms to do arc consistency. It is also shown that they all have optimal time complexity. The results of running the parallel algorithms on a BBN Butterfly multiprocessor are also presented.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Utah, Salt Lake City (USA)

- OSTI Identifier:
- 6231811

- Resource Type:
- Journal Article

- Journal Name:
- Int. J. Parallel Program.; (United States)

- Additional Journal Information:
- Journal Volume: 16:5

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARALLEL PROCESSING; ALGORITHMS; ARRAY PROCESSORS; COMPUTER CODES; CONSTRAINTS; DATA TRANSMISSION; EFFICIENCY; FUNCTIONS; ITERATIVE METHODS; MEMORY DEVICES; PERFORMANCE; TASK SCHEDULING; COMMUNICATIONS; DATA PROCESSING; MATHEMATICAL LOGIC; PROCESSING; PROGRAMMING; 990210* - Supercomputers- (1987-1989)

### Citation Formats

```
Samal, A., and Henderson, T.
```*Parallel consistent labeling algorithms*. United States: N. p., 1987.
Web. doi:10.1007/BF01407901.

```
Samal, A., & Henderson, T.
```*Parallel consistent labeling algorithms*. United States. doi:10.1007/BF01407901.

```
Samal, A., and Henderson, T. Thu .
"Parallel consistent labeling algorithms". United States. doi:10.1007/BF01407901.
```

```
@article{osti_6231811,
```

title = {Parallel consistent labeling algorithms},

author = {Samal, A. and Henderson, T.},

abstractNote = {Mackworth and Freuder have analyzed the time complexity of several constraint satisfaction algorithms. Mohr and Henderson have given new algorithms, AC-4 and PC-3, for arc and path consistency, respectively, and have shown that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms. In this paper, they give parallel algorithms for solving node and arc consistency. They show that any parallel algorithm for enforcing arc consistency in the worst case must have O(na) sequential steps, where n is number of nodes, and a is the number of labels per node. They give several parallel algorithms to do arc consistency. It is also shown that they all have optimal time complexity. The results of running the parallel algorithms on a BBN Butterfly multiprocessor are also presented.},

doi = {10.1007/BF01407901},

journal = {Int. J. Parallel Program.; (United States)},

number = ,

volume = 16:5,

place = {United States},

year = {1987},

month = {10}

}