Araştırma Makalesi

### A New Approach Based on Centrality Value in Solving the Maximum Independent Set Problem: Malatya Centrality Algorithm

Yıl 2023, Cilt: Vol:8 Sayı: Issue:1, 16 - 23, 08.06.2023

### Öz

Graph structure is widely used to describe problems in different fields. Problems in many areas, such as security and transportation, are among them. The problems can be solved using approaches similar to the graph structure. The independent set problem, which is NP-Complete problem, is one of the main problems of graph theory and is used in modeling many problems. The implementation of the Independent set problem with the most significant possible number of nodes in the graph is called the Maximum Independent set. A lot of algorithm approach are proposed to solve the problem. This study proposes an effective approach for the maximum independent problem. This approach occurs two steps: computing the Malatya centrality value and determining the maximum independent set. In the first step, centrality values are computed for the nodes forming the graph structure using the Malatya algorithm. The Malatya centrality value of the nodes in any graph is the sum of the ratios of the node's degree to the neighboring nodes' degrees. The second step is to determine the nodes to be selected for the maximum independent set problem. Here, the node with the minimum Malatya centrality value is selected and added to the independent set. Then, the edges of this node, its adjacent nodes, and the edges of adjacent nodes are subtracted from the graph. By repeating the new graph structure calculations, all vertexes are deleted so that the maximum independent set is determined. It is observed on the sample graph that the proposed approach provides an effecient solution for the maximum independent set. Successful test results and analyzes denonstrate the effectiveness of the proposed approach.

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### Kaynakça

• Alkhouri, I. R., Atia, G. K., & Velasquez, A. (2022). A differentiable approach to the maximum independent set problem using dataless neural networks. Neural Networks, 155, 168–176. Retrieved from https://doi.org/10.1016/j.neunet.2022.08.008
• Araujo, F., Farinha, J., Domingues, P., Silaghi, G. C., & Kondo, D. (2011). A maximum independent set approach for collusion detection in voting pools. Journal of Parallel and Distributed Computing, 71(10), 1356–1366. Retrieved from https://doi.org/10.1016/j.jpdc.2011.06.004
• Ballard-myer, J. C. (2019). Deterministic Greedy Algorithm for Maximum Independent Set Problem in Graph Theory, 1–14.
• Borgatti, S. P. (2005). Centrality and network flow. Social Networks, 27(1), 55–71. Retrieved from https://doi.org/10.1016/j.socnet.2004.11.008
• Brandstädt, A., & Mosca, R. (2018). Maximum weight independent set for lclaw-free graphs in polynomial time Discrete Applied Mathematics, 237, 57–64. Retrieved from https://doi.org/10.1016/j.dam.2017.11.029
• Cormen, T. H., Leiserson, C. E., Rivest, R., & Clifford, S. (2001). Introduction to algorithms (Introducti). London.
• Das, G. K., De, M., Kolay, S., Nandy, S. C., & Sur-Kolay, S. (2015). Approximation algorithms for maximum independent set of a unit disk graph. Information Processing Letters, 115(3), 439–446. Retrieved from https://doi.org/10.1016/j.ipl.2014.11.002
• Großmann, E., Lamm, S., Schulz, C., & Strash, D. (2022). Finding Near-Optimal Weight Independent Sets at Scale. Retrieved from http://arxiv.org/abs/2208.13645
• Joo, C., Lin, X., Ryu, J., & Shroff, N. B. (2016). Distributed Greedy Approximation to Maximum Weighted Independent Set for Scheduling With Fading Channels. IEEE/ACM Transactions on Networking, 24(3), 1476–1488. Retrieved from https://doi.org/10.1109/TNET.2015.2417861
• Karci, A. (2020). Efficient Algorithms for Determining the Maximum Independent Sets in Graphs. Computer Science, 5(2), 144–149.

### A New Approach Based on Centrality Value in Solving the Maximum Independent Set Problem: Malatya Centrality Algorithm

Yıl 2023, Cilt: Vol:8 Sayı: Issue:1, 16 - 23, 08.06.2023

### Öz

Graph structure is widely used to describe problems in different fields. Problems in many areas, such as security and transportation, are among them. The problems can be solved using approaches similar to the graph structure. The independent set problem, which is NP-Complete problem, is one of the main problems of graph theory and is used in modeling many problems. The implementation of the Independent set problem with the most significant possible number of nodes in the graph is called the Maximum Independent set. A lot of algorithm approach are proposed to solve the problem. This study proposes an effective approach for the maximum independent problem. This approach occurs two steps: computing the Malatya centrality value and determining the maximum independent set. In the first step, centrality values are computed for the nodes forming the graph structure using the Malatya algorithm. The Malatya centrality value of the nodes in any graph is the sum of the ratios of the node's degree to the neighboring nodes' degrees. The second step is to determine the nodes to be selected for the maximum independent set problem. Here, the node with the minimum Malatya centrality value is selected and added to the independent set. Then, the edges of this node, its adjacent nodes, and the edges of adjacent nodes are subtracted from the graph. By repeating the new graph structure calculations, all vertexes are deleted so that the maximum independent set is determined. It is observed on the sample graph that the proposed approach provides an effecient solution for the maximum independent set. Successful test results and analyzes denonstrate the effectiveness of the proposed approach.

-

### Kaynakça

• Alkhouri, I. R., Atia, G. K., & Velasquez, A. (2022). A differentiable approach to the maximum independent set problem using dataless neural networks. Neural Networks, 155, 168–176. Retrieved from https://doi.org/10.1016/j.neunet.2022.08.008
• Araujo, F., Farinha, J., Domingues, P., Silaghi, G. C., & Kondo, D. (2011). A maximum independent set approach for collusion detection in voting pools. Journal of Parallel and Distributed Computing, 71(10), 1356–1366. Retrieved from https://doi.org/10.1016/j.jpdc.2011.06.004
• Ballard-myer, J. C. (2019). Deterministic Greedy Algorithm for Maximum Independent Set Problem in Graph Theory, 1–14.
• Borgatti, S. P. (2005). Centrality and network flow. Social Networks, 27(1), 55–71. Retrieved from https://doi.org/10.1016/j.socnet.2004.11.008
• Brandstädt, A., & Mosca, R. (2018). Maximum weight independent set for lclaw-free graphs in polynomial time Discrete Applied Mathematics, 237, 57–64. Retrieved from https://doi.org/10.1016/j.dam.2017.11.029
• Cormen, T. H., Leiserson, C. E., Rivest, R., & Clifford, S. (2001). Introduction to algorithms (Introducti). London.
• Das, G. K., De, M., Kolay, S., Nandy, S. C., & Sur-Kolay, S. (2015). Approximation algorithms for maximum independent set of a unit disk graph. Information Processing Letters, 115(3), 439–446. Retrieved from https://doi.org/10.1016/j.ipl.2014.11.002
• Großmann, E., Lamm, S., Schulz, C., & Strash, D. (2022). Finding Near-Optimal Weight Independent Sets at Scale. Retrieved from http://arxiv.org/abs/2208.13645
• Joo, C., Lin, X., Ryu, J., & Shroff, N. B. (2016). Distributed Greedy Approximation to Maximum Weighted Independent Set for Scheduling With Fading Channels. IEEE/ACM Transactions on Networking, 24(3), 1476–1488. Retrieved from https://doi.org/10.1109/TNET.2015.2417861
• Karci, A. (2020). Efficient Algorithms for Determining the Maximum Independent Sets in Graphs. Computer Science, 5(2), 144–149.

### Ayrıntılar

Birincil Dil İngilizce Yazılım Mühendisliği, Yazılım Testi, Doğrulama ve Validasyon PAPERS Selman Yakut İNÖNÜ ÜNİVERSİTESİ Türkiye Furkan Öztemiz INONU UNIVERSITY, FACULTY OF ENGINEERING Türkiye Ali Karci INONU UNIVERSITY, FACULTY OF ENGINEERING Türkiye - 8 Haziran 2023 8 Haziran 2023 26 Aralık 2022 25 Ocak 2023 Yıl 2023 Cilt: Vol:8 Sayı: Issue:1

### Kaynak Göster

 APA Yakut, S., Öztemiz, F., & Karci, A. (2023). A New Approach Based on Centrality Value in Solving the Maximum Independent Set Problem: Malatya Centrality Algorithm. Computer Science, Vol:8(Issue:1), 16-23. https://doi.org/10.53070/bbd.1224520