### 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).

Original language | English |
---|---|

Pages (from-to) | 249-261 |

Number of pages | 13 |

Journal | Mathematics in Computer Science |

Volume | 10 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jun 2016 |

### Fingerprint

### Keywords

- Active membrane systems
- Minimum dominating set
- P systems
- Parallel computing

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Computational Theory and Mathematics

### Cite this

*Mathematics in Computer Science*,

*10*(2), 249-261. https://doi.org/10.1007/s11786-016-0261-5

**Membrane Computing to Enhance Time Efficiency of Minimum Dominating Set.** / Mahmood, Ali Abdulkareem; Maroosi, Ali; Muniyandi, Ravie Chandren.

Research output: Contribution to journal › Article

*Mathematics in Computer Science*, vol. 10, no. 2, pp. 249-261. https://doi.org/10.1007/s11786-016-0261-5

}

TY - JOUR

T1 - Membrane Computing to Enhance Time Efficiency of Minimum Dominating Set

AU - Mahmood, Ali Abdulkareem

AU - Maroosi, Ali

AU - Muniyandi, Ravie Chandren

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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(kn) 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(n2) 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).

AB - 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(kn) 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(n2) 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).

KW - Active membrane systems

KW - Minimum dominating set

KW - P systems

KW - Parallel computing

UR - http://www.scopus.com/inward/record.url?scp=84961647418&partnerID=8YFLogxK

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U2 - 10.1007/s11786-016-0261-5

DO - 10.1007/s11786-016-0261-5

M3 - Article

AN - SCOPUS:84961647418

VL - 10

SP - 249

EP - 261

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

SN - 1661-8270

IS - 2

ER -