This study employs clustering analysis to evaluate the efficiency of GPUs used in cryptocurrency mining, categorizing them into distinct groups based on computational output and power consumption. Using K-Means clustering, GPUs were grouped into three clusters: low-efficiency, moderate-efficiency, and high-efficiency. High-efficiency GPUs demonstrated superior hash rates (e.g., 104.79 Mh/s for AbelHash and 218.35 Mh/s for Autolykos2) despite higher power consumption, making them ideal for high-performance mining operations. Conversely, low-efficiency GPUs exhibited lower computational output and modest energy use, highlighting opportunities for hardware upgrades or repurposing. Visualization techniques, including scatter plots and pair plots, provided clear distinctions between clusters, while a silhouette score of 0.35 indicated moderate cluster separation, suggesting areas for further refinement. The findings offer actionable insights for optimizing hardware selection, reducing operational costs, and improving energy efficiency in mining operations. Additionally, this study underscores the importance of sustainability in cryptocurrency mining and provides a foundation for future research, including the integration of additional performance metrics, exploration of alternative clustering algorithms, and development of energy-efficient mining practices. These insights contribute to the broader goal of fostering a more sustainable and data-driven approach to cryptocurrency mining.
The environmental impact of Bitcoin mining in Kazakhstan, which is currently the third-largest market in the world by hash rate, is coming under further scrutiny. Data on the production of renewable energy and related carbon footprints are essential for evaluating the situation. To create a thorough picture of how Bitcoin mining and environmental responsibility connect in Kazakhstan, this paper allows for the analysis and prediction of the interactions between carbon emissions, renewable energy use, and Bitcoin mining. Using a q-rung orthopair fuzzy hypersoft set (q-ROFHS)-based multi-criteria decision-making technique can improve research on the environmental effects of Bitcoin mining, the integration of renewable energy sources, and the corresponding carbon footprints. The analytic hierarchy process is used to identify the best pollution reduction strategies while taking feasibility and cost-effectiveness into account. The proposed approach will assist the business in achieving its environmental objectives, lessen its negative effects on the environment, and promote a greener future. This study guarantees a more precise and dependable evaluation of pollution control tactics, considering not only the effects on the environment but also practicality and affordability. The outcomes highlight the developed approach's effectiveness and stability in managing complicated information within the parameters of q-ROFHS.
Partial orders and directed acyclic graphs are common data structures that arise naturally in numerous applications, and that define order between data points. Examples are orders of tasks in a project plan, transaction orders in distributed ledgers and execution sequences in computer programs, to mention a few.\nOn the other hand, hierarchical clustering is one of the oldest and most used methods for unsupervised classification and exploratory data analysis. In spite of this, few methods are rigged to take into account the information encoded in the order relation when performing hierarchical clustering of partially ordered data.\nIn his research, Daniel R. Bakkelund has developed new mathematical theory and algorithms to include this information in methods for hierarchical clustering, resulting in the concept of "order preserving hierarchical clustering".\nThe efficacy of theories are demonstrated through experiments on real world data, and show that the in comparison with existing methods, the new methods excel both in cluster quality and order preservation.
Abstract Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task dependencies in a project plan, transaction order in distributed ledgers and execution sequences of tasks in computer programs, just to mention a few. We study the problem of order preserving hierarchical clustering of this kind of ordered data. That is, if we have $$a<b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:mo><</mml:mo><mml:mi>b</mml:mi></mml:mrow></mml:math> in the original data and denote their respective clusters by [ a ] and [ b ], then we shall have $$[a]<[b]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mi>a</mml:mi><mml:mo>]</mml:mo><mml:mo><</mml:mo><mml:mo>[</mml:mo><mml:mi>b</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math> in the produced clustering. The clustering is similarity based and uses standard linkage functions, such as single- and complete linkage, and is an extension of classical hierarchical clustering. To achieve this, we develop a novel theory that extends classical hierarchical clustering to strictly partially ordered sets. We define the output from running classical hierarchical clustering on strictly ordered data to be partial dendrograms ; sub-trees of classical dendrograms with several connected components. We then construct an embedding of partial dendrograms over a set into the family of ultrametrics over the same set. An optimal hierarchical clustering is defined as the partial dendrogram corresponding to the ultrametric closest to the original dissimilarity measure, measured in the p -norm. Thus, the method is a combination of classical hierarchical clustering and ultrametric fitting. A reference implementation is employed for experiments on both synthetic random data and real world data from a database of machine parts. When compared to existing methods, the experiments show that our method excels both in cluster quality and order preservation.