Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/31424
Appears in Collections:Computing Science and Mathematics Book Chapters and Sections
Title: Finding the Maximal Independent Sets of a Graph Including the Maximum Using a Multivariable Continuous Polynomial Objective Optimization Formulation
Author(s): Heal, Maher
Li, Jingpeng
Contact Email: jingpeng.li@stir.ac.uk
Editor(s): Arai, Kohei
Kapoor, Supriya
Bhatia, Rahul
Citation: Heal M & Li J (2020) Finding the Maximal Independent Sets of a Graph Including the Maximum Using a Multivariable Continuous Polynomial Objective Optimization Formulation. In: Arai K, Kapoor S & Bhatia R (eds.) Intelligent Computing. SAI 2020. Advances in Intelligent Systems and Computing, 1228. Cham, Switzerland: Springer International Publishing, pp. 122-136. https://doi.org/10.1007/978-3-030-52249-0_9
Keywords: Independent set
Continuous optimization
MATLAB
Maximal cliques
Sparse graphs
Issue Date: 2020
Series/Report no.: Advances in Intelligent Systems and Computing, 1228
Abstract: We propose a multivariable continuous polynomial optimization formulation to find arbitrary maximal independent sets of any size for any graph. A local optima of the optimization problem yields a maximal independent set, while the global optima yields a maximum independent set. The solution is two phases. The first phase is listing all the maximal cliques of the graph and the second phase is solving the optimization problem. We believe that our algorithm is efficient for sparse graphs, for which there exist fast algorithms to list their maximal cliques. Our algorithm was tested on some of the DIMACS maximum clique benchmarks and produced results efficiently. In some cases our algorithm outperforms other algorithms, such as cliquer.
Rights: This item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. This is a post-peer-review, pre-copyedit version of a paper published in Arai K, Kapoor S & Bhatia R (eds.) Intelligent Computing. SAI 2020. Advances in Intelligent Systems and Computing, 1228. Cham, Switzerland: Springer International Publishing, pp. 122-136. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-52249-0_9
DOI Link: 10.1007/978-3-030-52249-0_9
Licence URL(s): https://storre.stir.ac.uk/STORREEndUserLicence.pdf

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