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Membrane Computing to Enhance Time Efficiency of Minimum Dominating Set

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Abstract

Graph theory is widely used in numerous fields, such as, engineering, physics, social and biological sciences; linguistics etc. The minimum dominating set (MDS) problem is one of the main problems of algorithmic graph theory and has numerous applications especially in graph mining. Since it is NP-hard to solve the MDS problem approximately, much work has been dedicated to central and distributed approximation algorithms for restricted graph classes. In recent research exponential time \(O(k^{n})\) algorithms are used for some graph classes for solving the MDS problem. In the approach of using the algorithmic tile self-assembly model, the MDS problem has been solved in \(O(n^{2})\) steps. On the other hand, in the area of membrane computing, P systems introduce two levels of parallelism: every membrane works concurrently with other membranes,and, rules are applied in parallel in each membrane. This paper introduces an algorithm based on the parallelism feature of the P systems model for solving the MDS problem in linear time O(n).

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Acknowledgments

We thank the reviewers for their appropriate and constructive suggestions and for their proposed corrections to improve the manuscript. The work has been supported by the Science Fund of the MOSTI—Ministry of Science, Technology and Innovation (Malaysia; Grant Code: 01-01-02-SF1104).

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Authors and Affiliations

  1. Faculty of Information Science and Technology, Center of Software Technology and Management, University Kebangsaan Malaysia, 43000, Bangi, Selangor, Malaysia

    Ali Abdulkareem Mahmood & Ravie Chandren Muniyandi

  2. Department of Computer Engineering and Information Technology, University of Torbat-e Heydarieh, Torbat-e Heydarieh, Khorasan, Iran

    Ali Maroosi

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  1. Ali Abdulkareem Mahmood
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  2. Ali Maroosi
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  3. Ravie Chandren Muniyandi
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Correspondence to Ravie Chandren Muniyandi.

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Mahmood, A.A., Maroosi, A. & Muniyandi, R.C. Membrane Computing to Enhance Time Efficiency of Minimum Dominating Set. Math.Comput.Sci. 10, 249–261 (2016). https://doi.org/10.1007/s11786-016-0261-5

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  • DOI: https://doi.org/10.1007/s11786-016-0261-5

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