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A New Augmentation Based Algorithm for Extracting Maximal Chordal Subgraphs.

Sanjukta Bhowmick¹, Tzu-Yi Chen², Mahantesh Halappanavar¹

¹University of Nebraska, Omaha; PKI 1110 South 67th St; Omaha, Nebraska, 68182.

Journal of Parallel and Distributed Computing

|March 14, 2015

Summary

This summary is machine-generated.

This study introduces a new parallel algorithm for finding maximal chordal subgraphs, overcoming limitations of previous sequential methods. The developed algorithm ensures maximality and demonstrates scalability for complex graph problems.

Keywords:

maximal chordal subgraphs parallel graph algorithms

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Area of Science:

Graph Theory
Parallel Algorithms
Computational Complexity

Background:

Chordal graphs are crucial for solving NP-hard problems efficiently.
Maximal chordal subgraphs have applications in various scientific domains.
Existing sequential algorithms limit parallelizability.

Purpose of the Study:

Develop a scalable parallel algorithm for extracting maximal chordal subgraphs.
Address limitations of previous parallel attempts.
Ensure the algorithm guarantees maximality.

Main Methods:

Propose a new algorithm based on computing and augmenting a spanning chordal subgraph.
Analyze the algorithm's termination and maximality.
Implement and evaluate a parallel version of the algorithm.

Main Results:

The new algorithm is proven to terminate with a maximal chordal subgraph.
The parallel version is more amenable to parallelization than previous methods.
Experimental results show scalability on synthetic and real-world graphs.

Conclusions:

The augmentation-based parallel algorithm effectively extracts maximal chordal subgraphs.
This approach offers a scalable solution for complex graph analysis.
Further research can explore initial spanning chordal subgraph choices for performance optimization.