A new augmentation based algorithm for extracting maximal chordal subgraphs
- Univ. of Nebraska, Omaha, NE (United States)
- Pomona College, Claremont, CA (United States)
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
If every cycle of a graph is chordal length greater than three then it contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard 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 non-optimal 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 augmentation-based algorithm on both synthetic and real-world 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.
- Research Organization:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC05-76RL01830; ACO6-76RL01830
- OSTI ID:
- 1184895
- Alternate ID(s):
- OSTI ID: 1249876
- Report Number(s):
- PNNL-SA-106337; 400470000
- Journal Information:
- Journal of Parallel and Distributed Computing, Vol. 76, Issue C; ISSN 0743-7315
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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