### 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 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 sub graph from a general graph. We develop an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it per iteration and 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 test set of synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies and demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.

Original language | English (US) |
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Title of host publication | Proceedings - 41st International Conference on Parallel Processing, ICPP 2012 |

Pages | 58-67 |

Number of pages | 10 |

DOIs | |

State | Published - Dec 20 2012 |

Event | 41st International Conference on Parallel Processing, ICPP 2012 - Pittsburgh, PA, United States Duration: Sep 10 2012 → Sep 13 2012 |

### Publication series

Name | Proceedings of the International Conference on Parallel Processing |
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ISSN (Print) | 0190-3918 |

### Conference

Conference | 41st International Conference on Parallel Processing, ICPP 2012 |
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Country | United States |

City | Pittsburgh, PA |

Period | 9/10/12 → 9/13/12 |

### Fingerprint

### Keywords

- chordal graphs
- large scale networks
- multithreaded algorithms

### ASJC Scopus subject areas

- Software
- Mathematics(all)
- Hardware and Architecture

### Cite this

*Proceedings - 41st International Conference on Parallel Processing, ICPP 2012*(pp. 58-67). [6337567] (Proceedings of the International Conference on Parallel Processing). https://doi.org/10.1109/ICPP.2012.10

**A novel multithreaded algorithm for extracting maximal chordal subgraphs.** / Halappanavar, Mahantesh; Feo, John; Cooper, Kathryn M; Ali, Hesham H; Bhowmick, Sanjukta.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 41st International Conference on Parallel Processing, ICPP 2012.*, 6337567, Proceedings of the International Conference on Parallel Processing, pp. 58-67, 41st International Conference on Parallel Processing, ICPP 2012, Pittsburgh, PA, United States, 9/10/12. https://doi.org/10.1109/ICPP.2012.10

}

TY - GEN

T1 - A novel multithreaded algorithm for extracting maximal chordal subgraphs

AU - Halappanavar, Mahantesh

AU - Feo, John

AU - Cooper, Kathryn M

AU - Ali, Hesham H

AU - Bhowmick, Sanjukta

PY - 2012/12/20

Y1 - 2012/12/20

N2 - Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing 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 sub graph from a general graph. We develop an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it per iteration and 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 test set of synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies and demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.

AB - Chordal graphs are triangulated graphs where any cycle larger than three is bisected by a chord. Many combinatorial optimization problems such as computing 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 sub graph from a general graph. We develop an iterative approach where each thread can asynchronously update a subset of edges that are dynamically assigned to it per iteration and 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 test set of synthetical graphs with up to half-a-billion edges and real world networks from gene correlation studies and demonstrate that our algorithm achieves high scalability for all inputs on both types of architectures.

KW - chordal graphs

KW - large scale networks

KW - multithreaded algorithms

UR - http://www.scopus.com/inward/record.url?scp=84871155052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871155052&partnerID=8YFLogxK

U2 - 10.1109/ICPP.2012.10

DO - 10.1109/ICPP.2012.10

M3 - Conference contribution

AN - SCOPUS:84871155052

SN - 9780769547961

T3 - Proceedings of the International Conference on Parallel Processing

SP - 58

EP - 67

BT - Proceedings - 41st International Conference on Parallel Processing, ICPP 2012

ER -