SavedAdd your journal

Journals / Bilgisayar Bilimleri / 2023 / Cilt: Vol:8 Sayı: Issue:1

Calculating the Centrality Values According to the Strengths of Entities Relative to their Neighbours and Designing a New Algorithm for the Solution of the Minimal Dominating Set Problem

Şeyda KARCI
Fatih OKUMUŞ
Ali KARCİ
Pages
50–56
Publication Date
2023-06-08
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The improved algorithms have polynomial time and space complexities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The dominating set problem in graph theory is an NP-complete problem for an arbitrary graph.
📊
Key Findings & Data:There are many approximation-based studies in the literature to solve the dominating set problems for a given graph.
💡
Conclusion & Impact:The improved algorithms have polynomial time and space complexities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Dominating Set · Malatya Centrality Value · Graph Theory

Abstract

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.

Özet

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.

🔖

Cite This Article

KARCI, Ş., OKUMUŞ, F., KARCİ, A. (2023). Calculating the Centrality Values According to the Strengths of Entities Relative to their Neighbours and Designing a New Algorithm for the Solution of the Minimal Dominating Set Problem. Bilgisayar Bilimleri, Cilt: Vol:8 Sayı: Issue:1, 50–56. https://ajindex.com/articles/945454

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. 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.
  2. Goddard, W., Henning, M.A.,”Independent domination in graphs: A survey and recent results”, Discrete Mathematics, Vol:313, pp:839-854, 2013.
  3. Grandoni, F.,”A note on the complexity of minimum dominating set”, Journal of Discrete Algorithms, Vol:4, pp:209-214, 2006.
  4. Guha, S., Khuller, S.,”Approximation Algorithms for Connected Dominating Sets”, Algorithmica, Vol:20, pp:374-387, 1998.
  5. Hagerup, T., “A strengthened analysis of an algorithm for Dominating Set in planar graphs”, Discrete Applied Mathematics, Vol:160, pp:793-798, 2012.
  6. 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.
  7. 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.
  8. Khuller, S., Yang, S.,” Revisiting Connected Dominating Sets: An Almost Optimal Local Information Algorithm”, Algorithmica, Vol:81, pp:2592-2605, 2019.
  9. Van Rooij, J.M.M., Bodlaender, H.L.,” Exact algorithms for dominating set”, Discrete Applied Mathematics, Vol:159, pp:2147-2164, 2011.
  10. Wawrzyniak, W.,”A local approximation algorithm for minimum dominating set problem in anonymous planar networks”, Distributed Computing, Vol:28, pp:321-331, 2015.