A Novel Multithreaded Algorithm for Extracting Maximal Chordal Subgraphs

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 t...

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Bibliographic Details
Published in:2012 41st International Conference on Parallel Processing pp. 58 - 67
Main Authors: Halappanavar, M., Feo, J., Dempsey, K., Ali, H., Bhowmick, S.
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2012
Subjects:
Algorithm design and analysis
Biology
chordal graphs
Correlation
Instruction sets
large scale networks
multithreaded algorithms
Partitioning algorithms
Sockets
ISBN:9781467325080, 1467325082
ISSN:0190-3918
Online Access:Get full text
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Summary: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.
ISBN:9781467325080
1467325082
ISSN:0190-3918
DOI:10.1109/ICPP.2012.10