# A Novel Multithreaded Algorithm For Extracting Maximal Chordal Subgraphs

## Abstract

Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing the minimum fill-in, the size of the maximum clique and the chromatic number are NP-hard on general graphs but have polynomial time solutions on chordal graphs. In this paper, we present a novel multithreaded algorithm to extract a maximal chordal subgraph from a general graph. Our algorithm is based on an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it. We implement our algorithm on two different multithreaded architectures – Cray XMT, a massively multithreaded platform, and AMD Magny-Cours, a shared memory multicore platform. In addition to the proof of correctness, we present the performance of our algorithm using a testset of carefully generated synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies. We demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1054479

- Report Number(s):
- PNNL-SA-85602

400470000

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Conference

- Resource Relation:
- Conference: 41st International Conference on Parallel Processing (ICPP), September 10-13, 2012, Pittsburgh, Pennsylvania, 58-67

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Halappanavar, Mahantesh, Feo, John T., Dempsey, Kathryn, Ali, Hesham, and Bhowmick, Sanjukta.
```*A Novel Multithreaded Algorithm For Extracting Maximal Chordal Subgraphs*. United States: N. p., 2012.
Web. doi:10.1109/ICPP.2012.10.

```
Halappanavar, Mahantesh, Feo, John T., Dempsey, Kathryn, Ali, Hesham, & Bhowmick, Sanjukta.
```*A Novel Multithreaded Algorithm For Extracting Maximal Chordal Subgraphs*. United States. doi:10.1109/ICPP.2012.10.

```
Halappanavar, Mahantesh, Feo, John T., Dempsey, Kathryn, Ali, Hesham, and Bhowmick, Sanjukta. Thu .
"A Novel Multithreaded Algorithm For Extracting Maximal Chordal Subgraphs". United States. doi:10.1109/ICPP.2012.10.
```

```
@article{osti_1054479,
```

title = {A Novel Multithreaded Algorithm For Extracting Maximal Chordal Subgraphs},

author = {Halappanavar, Mahantesh and Feo, John T. and Dempsey, Kathryn and Ali, Hesham and Bhowmick, Sanjukta},

abstractNote = {Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing the minimum fill-in, the size of the maximum clique and the chromatic number are NP-hard on general graphs but have polynomial time solutions on chordal graphs. In this paper, we present a novel multithreaded algorithm to extract a maximal chordal subgraph from a general graph. Our algorithm is based on an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it. We implement our algorithm on two different multithreaded architectures – Cray XMT, a massively multithreaded platform, and AMD Magny-Cours, a shared memory multicore platform. In addition to the proof of correctness, we present the performance of our algorithm using a testset of carefully generated synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies. We demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.},

doi = {10.1109/ICPP.2012.10},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {10}

}