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Title: 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}
}

Conference:
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