Teorik Makale

The dominating set problem in graph theory is an NP-complete problem for an arbitrary graph. There are many approximation-based studies in the literature to solve the dominating set problems for a given graph. Some of them are exact algorithms with exponential time complexities and some of them are based on approximation without robustness with respect to obtained solutions. In this study, the Malatya centrality value was used and a new Malatya centrality value was defined to solve the dominating set problem for a given graph. The improved algorithms have polynomial time and space complexities.

Dominating Set Malatya Centrality Value Graph Theory NP-Complete Problem

- Bourgeois, N., Croce, F.D., Escoffier, B., Paschos, V.T.,” Fast algorithms for min independent dominating set”, Discrete Applied Mathematics, Vol:161, pp:558-572, 2013.
- Goddard, W., Henning, M.A.,”Independent domination in graphs: A survey and recent results”, Discrete Mathematics, Vol:313, pp:839-854, 2013.
- Grandoni, F.,”A note on the complexity of minimum dominating set”, Journal of Discrete Algorithms, Vol:4, pp:209-214, 2006.
- Guha, S., Khuller, S.,”Approximation Algorithms for Connected Dominating Sets”, Algorithmica, Vol:20, pp:374-387, 1998.
- Hagerup, T., “A strengthened analysis of an algorithm for Dominating Set in planar graphs”, Discrete Applied Mathematics, Vol:160, pp:793-798, 2012.
- Karci, A., Yakut, S., Oztemiz, F.,” A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm”, Journal of Computer Science, Vol:7, pp:81-88,2022.
- Khamis, S.M., Daoud, S.S., Essa, H.A.E,” A randomized algorithm for determining dominating sets in graphs of maximum degree five”, Theoretical Computer Science, Vol:410, pp:5122-5127, 2009.
- Khuller, S., Yang, S.,” Revisiting Connected Dominating Sets: An Almost Optimal Local Information Algorithm”, Algorithmica, Vol:81, pp:2592-2605, 2019.
- Van Rooij, J.M.M., Bodlaender, H.L.,” Exact algorithms for dominating set”, Discrete Applied Mathematics, Vol:159, pp:2147-2164, 2011.
- Wawrzyniak, W.,”A local approximation algorithm for minimum dominating set problem in anonymous planar networks”, Distributed Computing, Vol:28, pp:321-331, 2015.

The dominating set problem in graph theory is an NP-complete problem for an arbitrary graph. There are many approximation-based studies in the literature to solve the dominating set problems for a given graph. Some of them are exact algorithms with exponential time complexities and some of them are based on approximation without robustness with respect to obtained solutions. In this study, the Malatya centrality value was used and a new Malatya centrality value was defined to solve the dominating set problem for a given graph. The improved algorithms have polynomial time and space complexities.

Dominating Set Malatya Centrality Value Graph Theory NP-Complete Problem

- Bourgeois, N., Croce, F.D., Escoffier, B., Paschos, V.T.,” Fast algorithms for min independent dominating set”, Discrete Applied Mathematics, Vol:161, pp:558-572, 2013.
- Goddard, W., Henning, M.A.,”Independent domination in graphs: A survey and recent results”, Discrete Mathematics, Vol:313, pp:839-854, 2013.
- Grandoni, F.,”A note on the complexity of minimum dominating set”, Journal of Discrete Algorithms, Vol:4, pp:209-214, 2006.
- Guha, S., Khuller, S.,”Approximation Algorithms for Connected Dominating Sets”, Algorithmica, Vol:20, pp:374-387, 1998.
- Hagerup, T., “A strengthened analysis of an algorithm for Dominating Set in planar graphs”, Discrete Applied Mathematics, Vol:160, pp:793-798, 2012.
- Karci, A., Yakut, S., Oztemiz, F.,” A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm”, Journal of Computer Science, Vol:7, pp:81-88,2022.
- Khamis, S.M., Daoud, S.S., Essa, H.A.E,” A randomized algorithm for determining dominating sets in graphs of maximum degree five”, Theoretical Computer Science, Vol:410, pp:5122-5127, 2009.
- Khuller, S., Yang, S.,” Revisiting Connected Dominating Sets: An Almost Optimal Local Information Algorithm”, Algorithmica, Vol:81, pp:2592-2605, 2019.
- Van Rooij, J.M.M., Bodlaender, H.L.,” Exact algorithms for dominating set”, Discrete Applied Mathematics, Vol:159, pp:2147-2164, 2011.
- Wawrzyniak, W.,”A local approximation algorithm for minimum dominating set problem in anonymous planar networks”, Distributed Computing, Vol:28, pp:321-331, 2015.

Toplam 10 adet kaynakça vardır.

Birincil Dil | İngilizce |
---|---|

Konular | Bilgisayar Yazılımı, Yazılım Testi, Doğrulama ve Validasyon |

Bölüm | PAPERS |

Yazarlar | |

Erken Görünüm Tarihi | 8 Haziran 2023 |

Yayımlanma Tarihi | 8 Haziran 2023 |

Gönderilme Tarihi | 14 Mayıs 2023 |

Kabul Tarihi | 2 Haziran 2023 |

Yayımlandığı Sayı | Yıl 2023 Cilt: Vol:8 Sayı: Issue:1 |

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