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Öğe A Graph-Theoretic Solution to NP-Complete Sudoku Puzzles: Malatya Centrality for Large-Scale Optimization(Ieee-Inst Electrical Electronics Engineers Inc, 2025) Yakut, Selman; Karagoz, ErkanThe sudoku puzzle, an NP-complete problem, presents significant computational challenges due to its constrained structure and vast solution space. While widely studied in artificial intelligence and optimization, existing methods often struggle with scalability and varying difficulty levels. This study introduces a novel, graph coloring-based approach leveraging the Malatya centrality algorithm to efficiently solve sudoku puzzles. By transforming the sudoku board into a graph, we compute node centrality values to guide the coloring process, where distinct color clusters correspond to numerical solutions. Our method was rigorously evaluated on datasets consisting of up to 1,000,000 puzzles and achieved 100% accuracy. It has achieved successful results when compared to other methods across various difficulty levels (easy, medium, and hard). This represents a significant advancement over traditional techniques (e.g., genetic algorithms, constraint propagation) and classical graph colouring methods (Brute Force, DSatur, Welsh Powell, etc.).The Malatya centrality algorithm's robust-ness stems from its centrality-driven prioritization, enabling optimal resource allocation during search. Furthermore, we demonstrate its potential for broader applications, including complex network analysis and combinatorial optimization. This work not only advances sudoku-solving methodologies but also provides a framework for integrating graph-theoretic centrality measures into NP-complete problem domains. Future directions include adaptations to real-world problems such as scheduling, bioinformatics, and social network analysis.Öğe A robust and efficient algorithm for graph coloring problem based on Malatya centrality and sequent independent sets(Cairo Univ, Fac Computers & Information, 2025) Yakut, SelmanThe Graph Coloring Problem (GCP) is an NP-hard problem that aims to color the vertices of a graph using the minimum number of distinct colors, ensuring that adjacent vertices do not share the same color. GCP is widely applied in real-world scenarios and graph theory problems. Despite numerous studies on solving GCP, existing methods face limitations, often performing well on specific graph types but failing to deliver efficient solutions across diverse structures. This study introduces the Malatya Sequent Independent Set Coloring Algorithm as an effective solution for GCP. The algorithm utilizes the Malatya Centrality Algorithm to compute Malatya Centrality (MC) values for graph vertices, where an MC value is defined as the sum of the ratios of a vertex's degree to its neighbors' degrees. The algorithm selects the vertex with the lowest MC value, adds it to an independent set, and removes it along with its neighbors and edges. This process repeats until the first sequent independent set is identified. The removed set is then excluded from the original graph, and the process continues on the remaining structure to determine additional sequent independent sets, ensuring that each set corresponds to a single color group in GCP. The algorithm was tested on social network graphs, random graphs, and benchmark datasets, supported by mathematical analyses and proofs. The results confirm that the algorithm provides efficient, polynomial-time solutions for GCP and maintains high performance across various graph types, independent of constraints.Öğe An Effective Approach Based on the Malatya Centrality Algorithm for Determining the Maximum Independent Set and Minimum Vertex Cover in Molecular Graphs(Institute of Electrical and Electronics Engineers Inc., 2024) Yakut, SelmanMolecular graphs are graphs formed by considering atoms as nodes and the connections between these atoms as edges, which constitute the structure of chemical compounds. These graphs are used to analyze the chemical and structural properties of molecules. In this study, an effective and robust approach based on the Malatya Centrality algorithm is proposed for determining the maximum independent set and the minimum vertex cover in molecular graphs. In the proposed approach, the molecular graph is transformed into a graph structure consisting of nodes and edges. Subsequently, Malatya centrality values are computed for the nodes in this graph. Using these values, the maximum independent set is first calculated for the molecular graph. Then, utilizing this set, the minimum vertex cover for the molecular graph is determined. To demonstrate the effectiveness of the proposed approach, tests and analyses were conducted on molecular graphs of various sizes, complexities, and classes. The successful test results and analyses indicate that the proposed approach is an effective and robust method for determining the maximum independent set and the minimum vertex cover in molecular graphs. © 2024 IEEE.Öğe An Effective Method for Determining Node Dominance Values: Malatya Centrality Algorithm(Ieee, 2024) Oztemiz, Furkan; Yakut, SelmanCentrality is a frequently used metric in graph theory that identifies the dominance values of nodes. In this study, the Malatya Centrality Algorithm, which approaches graph centrality from a new perspective, has been proposed. To calculate the centrality of a node in the graph, the ratio of the node's degree to the degrees of its neighboring nodes was computed and these ratios were summed. The results of the proposed algorithm were compared with established centrality algorithms in the literature and tested on well-known social networks such as Zachary's karate club, the dolphin social network, and the zebra network. The tests and analyses conducted demonstrate that the Malatya Centrality Algorithm is an effective and successful centrality algorithm.Öğe Efficient and Robust Graph Coloring Algorithm for Graph Coloring Problem: Malatya Vertex Coloring Algorithm(Ieee-Inst Electrical Electronics Engineers Inc, 2025) Yakut, SelmanThe graph coloring problem involves coloring the nodes of a graph using the minimum number of colors such that no two adjacent nodes share the same color. This NP-hard problem has various real-world applications, including scheduling problems, map coloring, and resource allocation. Although numerous algorithms have been proposed in the literature to solve this problem, there is a lack of effective and robust algorithms that perform well across different types of graphs. In this study, we propose the Malatya Vertex Coloring Algorithm, an efficient and robust solution for the graph coloring problem. The proposed algorithm calculates the Malatya centrality value for each node by summing the ratios of the node's degree to the degrees of its neighboring nodes. Starting from the node with the highest Malatya centrality value, the graph is colored such that each node is assigned a color different from its neighbors. The effectiveness of the proposed algorithm is demonstrated through extensive testing and analysis. First, experiments were conducted on benchmark graphs from the literature, varying in size and complexity based on the number of nodes and edges. Additionally, tests were performed on social network graphs (which model social connections and behaviors) as well as randomly generated graphs with different densities and sizes. The results show that the proposed algorithm outperforms well-known existing methods such as Welsh-Powell, Greedy Coloring, DSatur, and RLF in terms of efficiency, robustness, and success rate. Moreover, in some graph types, it yields better results than MSISCA, another efficient and robust algorithm. It is mathematically proven that the proposed algorithm provides a solution in polynomial time for any arbitrary graph and guarantees an optimal solution for specific graph classes. The analyses and experimental results demonstrate that the Malatya Vertex Coloring Algorithm delivers effective and robust solutions for the graph coloring problem across various graph types without any constraints or parameter dependencies.Öğe Graf Teorisi ve Malatya Merkezilik Algoritmasına Dayalı Haber Metinlerinin Özetlemesi(2024) Yakut, Selman; Bakan, Cevher TayyibGünümüzde internetin yaygın kullanımıyla, bilgi kaynaklarındaki doğru bilgiye erişimi önemli kılmaktadır. Bilgi kaynaklarının artmasıyla birlikte özgün içeriğe sahip bilgiye erişim güçleşmektedir. Bu nedenle metin özetleme yöntemlerinin önemi giderek artmaktadır. Haber metinleri gibi önemli temel bilgi kaynaklarının etkili bir şekilde özetlenmesi günümüzde bir gereklilik haline gelmiştir. Bu çalışmada haber metinlerinin etkili bir şekilde özetlenmesi için Malatya merkezilik algoritmasını temel alan bir özetleme yaklaşımı önerildi. Önerilen yaklaşımda orijinal metin tanımlayıcıların çıkarılması, kelime köklerinin elde edilmesi gibi çeşitli ön işlemlerden geçirilerek graf yapısına dönüştürülür. Graf’a dönüştürülen metin için Malatya merkezilik algoritması kullanılarak graftaki düğümlerin Malatya merkezilik değerleri hesaplanır. Bu değerler dikkate alınarak metin özetini oluşturan özetler seçilir. Seçilen özetler graftan çıkarılır. Oluşan yeni graf yapısı için merkezilik değeri hesaplanarak seçim işlemleri devam ettirilir. Graf Teorisi ve Malatya merkezilik algoritmasının birlikte kullanımı, haber metinlerinin özetlenmesinde verimliliği artırdığı gösterildi. Bununla birlikte haber içeriklerinin anlamlı bir şekilde özetlenmesi sağlandı. Bu yaklaşımın başarısını değerlendirmek amacıyla BBC veri seti üzerinde toplamda 2224 ingilizce haber metniyle kapsamlı bir şekilde test edildi. Çalışmada haber metinleri etkili bir şekilde özetlendiği yapılan testlerle ve alınan etkili rouge değerleriyle gösterildi. Graf teorisi ve Malatya merkezilik algoritması, bilgiye erişimi kolaylaştırmak ve anlam düzeyinde etkileşimi artırmak adına önemli bir potansiyele sahip olduğu gösterildi. Elde edilen uygulama sonuçları, haber metinlerini daha anlamlı bir şekilde sunabileceğini ve etkili özetler üretilebileceğini göstermektedir.Öğe KAYIPLI RESİM SIKIŞTIRMA ALGORİTMALARINI TEMEL ALAN RASTGELE SAYI ÜRETECİ(2022) Yakut, SelmanDijitalleşen dünyada veri güvenliği önemli bir problemdir. Veri güvenliğini sağlamak için çeşitli kriptoğrafik sistemler kullanılır. Rastgele sayılar ise bu sistemlerin önemli bir parçasıdır. Bu makalede resim sıkıştırma algoritmalarının temeli olan ayrık kosinüs dönüşümü kullanan bir rastgele sayı üreteci önerildi. Bu üreteçte öncelikle sıkıştırılacak olan resim, ayrık kosinüs dönüşümü ile frekans düzlemine aktarılır. Frekans uzayında insan görme duyusu dikkate alınarak resmi ifade eden belirli katsayılar dikkate alınıp diğerleri ihmal edildiğinden veri kaybı olur. Frakans uzayındaki veri ters ayrık kosinüs dönüşümüyle yeniden uzay düzlemine aktarılır. Bu dönüşüm esnasında hesaplanan küsuratlı değerler resmi ifade etmek için yuvarlanır. Yuvarlama esnasında bu veriler geriye döndürülemeyecek şekilde kaybedilir. Bu kayıp entropi kaynağı olarak kullanılarak ham rastgele sayılar üretildi. Bu sayılardaki olası zayıflıklar kriptografik özet fonksiyonu kullanılarak giderildi. Kriptografik özet fonksiyonu olarak SHA1 algoritması kullanıldı. Önerilen üreteç herhangi bir dijital veri kaynağını rastgele sayı üreteci olarak kullanabilir. Önerilen üretecin güvenliği yapılan testlerle ve analizlerle gösterildi.Öğe Kendall rank correlation analysis of Malatya Centrality Algorithm with well-known centrality measures(Yildiz Technical Univ, 2025) Yakut, Selman; Oztemiz, Furkan; Karci, AliThe concept of centrality is widely used in graph theory to determine the dominance of nodes within a graph. This concept is crucial for solving many real-life problems that are modeled using graphs. In this study, the effectiveness of a new approach, the Malatya Centrality Algorithm, for determining the centrality of nodes in a graph is examined. This algorithm provides effective solutions to problems in both graph theory and real-life applications. The centrality value in the Malatya Centrality Algorithm is calculated by summing the ratios of the degree of the relevant node to the degrees of its neighboring nodes. To demonstrate the effectiveness of the Malatya Centrality Algorithm, comparisons and analyses were conducted with well-known centrality algorithms in the literature. Various types of graphs, including random graphs, benchmark graphs, social network graphs, and lattice bipartite graphs, were used for these comparisons and analyses. Kendall rank correlation analysis and tests were performed on these different types of graphs for the Malatya Centrality Algorithm and the well-known centrality measures in the literature. The tests conducted on various graphs reveal the ranking of nodes based on their effectiveness. These rankings help identify nodes used in numerous problems. The tests and analyses demonstrate that the Malatya Centrality Algorithm produces results similar to those of established centrality algorithms in the literature and confirms its effectiveness across different types of graphs.Öğe Kısıt Optimizasyonu için Malatya Vertex Coloring Algoritması Kullanılarak Graf Tabanlı Ders Çizelgeleme(2025) Yakut, Selman; Karaca, CezayirDers çizelgeleme problemi, 20. yüzyılın ikinci yarısından itibaren araştırmacıların dikkatini çeken önemli bir kombinatoryal optimizasyon problemidir. Geleneksel olarak manuel yöntemlerle yürütülen çizelgeleme süreci, zaman alıcı ve zorlayıcı olmakla birlikte hata yapmaya açık bir yapıdadır. Bu nedenle, teknolojik ilerlemelerle birlikte çeşitli algoritmalar geliştirilerek daha etkili ve hızlı çözümler sunulmaya çalışılmıştır. Bu çalışmada, \"Malatya Vertex Coloring(MVC) Algoritması\" ders çizelgeleme problemine uygulanmaktadır. Algoritma, iki temel adımda çalışmaktadır: ilk olarak, çizelge grafındaki düğümlerin Malatya Merkezilik değerleri hesaplanmakta; ardından en yüksek merkeziliğe sahip düğüm seçilerek uygun bir renkle etiketlenmektedir. Süreç boyunca temel hedef, ders çakışmalarını en aza indirmek ve tanımlı kısıtlamalara uyumlu, geçerli bir çizelge üretmektir. MVC Algoritması, işlem adımlarının öngörülebilirliği ve polinom zamanda çalışabilme potansiyeliyle dikkat çekmekte, bu yönüyle literatürde önerilen klasik ve sezgisel yöntemlere etkili bir alternatif sunmaktadır.Öğe Malatya Centrality Algorithm and Graph Colouring Based Effective and Efficient Eight Queen Problem Solution Method(Institute of Electrical and Electronics Engineers Inc., 2025) Karagöz, Erkan; Yakut, SelmanThe eight queens problem, a classic constraint satisfaction problem in computer science, is a combinatorial problem that has been studied since the 19th century with applications to algorithm development, mathematical thinking and artificial intelligence. Briefly, the problem is to place eight queens on a chessboard in such a way that they do not threaten each other. Until today, the problem has been addressed with heuristic or brute force algorithms and now with artificial intelligence applications. Since the NP-Hard nature of the problem requires a large number of combinations to be tried, it is important to produce efficient algorithms. In this paper, we propose a method that solves the problem based on graph theory and centrality calculus. Firstly, each box on the chessboard is defined as a node. Considering the constraints of the problem, edge connections are established between these nodes and modelled as a graph. On this graph structure, the centrality calculations of the nodes were made with the Malatya Centrality algorithm. Then, starting from the node with the highest centrality value. The queens (colours) were placed in a regular way. As an alternative to classical methods, this method offers a perspective based on graph theory and graph colouring and creates a more systematic approach to queen placement. © 2025 IEEE.Öğe Malatya Düğüm Renklendirme Algoritması Kullanılarak Harita Renklendirme Problemi için Yenilikçi Bir Çözüm(2025) Yakut, Selman; Karaca, CezayirHarita renklendirme problemi, bitişik bölgelerin farklı renklerle boyanmasını gerektiren ve birçok gerçek hayat uygulamasında karşılaşılan klasik bir NP-tam problemdir. Bu problemin çözümü için birçok algoritma geliştirilmiştir. Bu çalışmada, ilgili problemin çözümüne yönelik yeni ve özgün bir yaklaşım ortaya koyan Malatya Vertex Coloring (MVC) Algoritması uygulanmıştır. Bu algoritma, graflarda kullanılan renk sayısını azaltmak için etkili düğümleri belirlemekte ve renklendirme sürecini daha kısa sürede tamamlamayı hedeflemektedir. Ayrıca algoritmanın, gerçek hayat problemlerine uygulanabilirliği de değerlendirilmiştir. MVC Algoritması, graf yapısındaki her düğüm için Malatya Merkezilik değerini hesaplar; en yüksek değere sahip düğümü seçerek komşularından farklı bir renkle boyar ve ardından bu düğümü graf üzerinden çıkarır. Bu işlem, tüm düğümler renklendirilene kadar devam etmektedir. Algoritma; Asya, Avrupa, İstanbul ilçeleri, Türkiye, ABD eyaletleri ve Dünya haritaları üzerinde başarıyla uygulanmış ve elde edilen sonuçlar algoritmanın etkinliğini ortaya koymuştur. MVC Algoritması’nın avantajları arasında öngörülebilir olması, polinom zamanda ve polinom uzayda çalışabilmesi yer almaktadır. Bu yönüyle, MVC Algoritması’nın harita renklendirme problemine ilişkin olarak klasik Dört Renk Teoremi’ne alternatif bir çözüm yaklaşımı sunduğu ortaya konulmuştur.Öğe A new robust approach to solve minimum vertex cover problem: Malatya vertex-cover algorithm(Springer, 2023) Yakut, Selman; Oeztemiz, Furkan; Karci, AliThe minimum vertex-cover problem (MVCP) is an NP-complete optimization problem widely used in areas such as graph theory, social network, security and transportation, etc. Different approaches and algorithms have been proposed in the literature to solve this problem, since MVCP is an optimization problem, the solutions developed for this problem could be more intuitive and give results under certain constraints. In addition, the proposed solution methods for this problem could be more effective, and the determined solution sets change in each iteration. The algorithms/methods developed for solving MVCP are mostly based on heuristic or greedy approaches. This study presents the Malatya vertex-cover algorithm, which provides an efficient solution and a robust approach based on the Malatya centrality value algorithm for MVCP. Although MVCP is an NP-complete problem that cannot be solved in polynomial time, the proposed method offers a polynomial solution to this problem, and the obtained solutions are optimum or near-optimum (optimal solution). This algorithm consists of two basic steps. In the first step, the Malatya centrality values of the nodes in the graph are calculated using the Malatya centrality algorithm. The Malatya centrality value of the nodes in any graph is the summation of the ratio of the node's degree to the adjacent nodes' degrees for each node. In the second step, nodes are selected for the MVCP solution based on the node with the maximum Malatya centrality value (psi) in the graph is selected and added to the solution set. Then this node and the edges incident on this node are removed from the graph. For the graph consisting of the remaining nodes, Malatya centrality values are calculated again, and the selection process is continued. The process is terminated when all edges in the graph are covered. The proposed algorithm has been tested on artificial, actual graphs and large-scale random graphs produced with the Erdos-Renyi model. When the results are examined, the proposed algorithm yields a robust solution set in polynomial time and polynomial space independent of constraints. In addition, the successful test results in the sample graphs and the analysis of the proposed approach show the effectiveness/superiority of the Malatya centrality algorithm and the proposed method.
