A new augmentation based algorithm for extracting maximal chordal subgraphs
If every cycle of a graph is chordal length greater than three then it contains an edge between nonadjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NPhard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms’ parallelizability. In our paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a nonoptimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. Thatmore »
 Authors:

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 Univ. of Nebraska, Omaha, NE (United States)
 Pomona College, Claremont, CA (United States)
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Publication Date:
 Report Number(s):
 PNNLSA106337
Journal ID: ISSN 07437315; 400470000
 Grant/Contract Number:
 AC0576RL01830; ACO676RL01830
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Parallel and Distributed Computing
 Additional Journal Information:
 Journal Volume: 76; Journal Issue: C; Journal ID: ISSN 07437315
 Publisher:
 Elsevier
 Research Org:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; chordal graphs; parallel algorithms
 OSTI Identifier:
 1184895
 Alternate Identifier(s):
 OSTI ID: 1249876
Bhowmick, Sanjukta, Chen, TzuYi, and Halappanavar, Mahantesh. A new augmentation based algorithm for extracting maximal chordal subgraphs. United States: N. p.,
Web. doi:10.1016/j.jpdc.2014.10.006.
Bhowmick, Sanjukta, Chen, TzuYi, & Halappanavar, Mahantesh. A new augmentation based algorithm for extracting maximal chordal subgraphs. United States. doi:10.1016/j.jpdc.2014.10.006.
Bhowmick, Sanjukta, Chen, TzuYi, and Halappanavar, Mahantesh. 2014.
"A new augmentation based algorithm for extracting maximal chordal subgraphs". United States.
doi:10.1016/j.jpdc.2014.10.006. https://www.osti.gov/servlets/purl/1184895.
@article{osti_1184895,
title = {A new augmentation based algorithm for extracting maximal chordal subgraphs},
author = {Bhowmick, Sanjukta and Chen, TzuYi and Halappanavar, Mahantesh},
abstractNote = {If every cycle of a graph is chordal length greater than three then it contains an edge between nonadjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NPhard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms’ parallelizability. In our paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a nonoptimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. Finally, we experimented with our augmentationbased algorithm on both synthetic and realworld graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.},
doi = {10.1016/j.jpdc.2014.10.006},
journal = {Journal of Parallel and Distributed Computing},
number = C,
volume = 76,
place = {United States},
year = {2014},
month = {10}
}