{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T12:45:46Z","timestamp":1770468346346,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T00:00:00Z","timestamp":1724371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NTHU","award":["113Q2714E1"],"award-info":[{"award-number":["113Q2714E1"]}]},{"name":"NTHU","award":["MOST 102-2221-E-007-086-MY3"],"award-info":[{"award-number":["MOST 102-2221-E-007-086-MY3"]}]},{"name":"NTHU","award":["MOST 104-2221-E-007-061-MY3"],"award-info":[{"award-number":["MOST 104-2221-E-007-061-MY3"]}]},{"name":"NTHU","award":["2023\/13667-5"],"award-info":[{"award-number":["2023\/13667-5"]}]},{"name":"Ministry of Science and Technology","award":["113Q2714E1"],"award-info":[{"award-number":["113Q2714E1"]}]},{"name":"Ministry of Science and Technology","award":["MOST 102-2221-E-007-086-MY3"],"award-info":[{"award-number":["MOST 102-2221-E-007-086-MY3"]}]},{"name":"Ministry of Science and Technology","award":["MOST 104-2221-E-007-061-MY3"],"award-info":[{"award-number":["MOST 104-2221-E-007-061-MY3"]}]},{"name":"Ministry of Science and Technology","award":["2023\/13667-5"],"award-info":[{"award-number":["2023\/13667-5"]}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"publisher","award":["113Q2714E1"],"award-info":[{"award-number":["113Q2714E1"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"publisher","award":["MOST 102-2221-E-007-086-MY3"],"award-info":[{"award-number":["MOST 102-2221-E-007-086-MY3"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"publisher","award":["MOST 104-2221-E-007-061-MY3"],"award-info":[{"award-number":["MOST 104-2221-E-007-061-MY3"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"publisher","award":["2023\/13667-5"],"award-info":[{"award-number":["2023\/13667-5"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["BDCC"],"abstract":"<jats:p>Data structures such as sets, lists, and arrays are fundamental in mathematics and computer science, playing a crucial role in numerous real-life applications. These structures represent a variety of entities, including solutions, conditions, and objectives. In scenarios involving large datasets, eliminating duplicate elements is essential to reduce complexity and enhance performance. This paper introduces a novel algorithm that uses logarithmic prime numbers to efficiently sort data structures and remove duplicates. The algorithm is mathematically rigorous, ensuring correctness and providing a thorough analysis of its time complexity. To demonstrate its practicality and effectiveness, we compare our method with existing algorithms, highlighting its superior speed and accuracy. An extensive experimental analysis across one thousand random test problems shows that our approach significantly outperforms two alternative techniques from the literature. By discussing the potential applications of the proposed algorithm in various domains, including computer science, engineering, and data management, we illustrate its adaptability through two practical examples in which our algorithm solves the problem more than 3\u00d7104 and 7\u00d7104 times faster than the existing algorithms in the literature. The results of these examples demonstrate that the superiority of our algorithm becomes increasingly pronounced with larger problem sizes.<\/jats:p>","DOI":"10.3390\/bdcc8090096","type":"journal-article","created":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T10:01:51Z","timestamp":1724666511000},"page":"96","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Efficient Algorithm for Sorting and Duplicate Elimination by Using Logarithmic Prime Numbers"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7393-0768","authenticated-orcid":false,"given":"Wei-Chang","family":"Yeh","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 300044, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1691-7633","authenticated-orcid":false,"given":"Majid","family":"Forghani-elahabad","sequence":"additional","affiliation":[{"name":"Center of Mathematics, Computing, and Cognition, Federal University of ABC, Santo Andr\u00e9 09280-560, S\u00e3o Paulo, Brazil"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,23]]},"reference":[{"key":"ref_1","first-page":"38","article-title":"An Analysis on Removal of Duplicate Records using Different Types of Data Mining Techniques: A Survey","volume":"6","author":"Selvi","year":"2017","journal-title":"Int. J. Comput. Sci. Mob. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109417","DOI":"10.1016\/j.ress.2023.109417","article-title":"Usage of task and data parallelism for finding the lower boundary vectors in a stochastic-flow network","volume":"238","author":"Francesquini","year":"2023","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Andriyanov, N., Dementev, V., Tashlinskiy, A., and Vasiliev, K. (2021). The Study of Improving the Accuracy of Convolutional Neural Networks in Face Recognition Tasks. Pattern Recognition, Springer. ICPR International Workshops and Challenges. ICPR 2021. Lecture Notes in Computer Science.","DOI":"10.1007\/978-3-030-68821-9_1"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Marsza\u0142ek, Z. (2017). Parallelization of Modified Merge Sort Algorithm. Symmetry, 9.","DOI":"10.3390\/sym9090176"},{"key":"ref_5","first-page":"3889","article-title":"An Efficient Technique for Removing Duplicates in A Dataset","volume":"2","author":"Raj","year":"2013","journal-title":"Int. J. Eng. Res. Technol."},{"key":"ref_6","unstructured":"Svitov, D., and Alyamkin, S. (2020). Margindistillation: Distillation for margin-based softmax. arXiv."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Sadanandan, I.T., and Chitturi, B. (2022). Optimal Algorithms for Sorting Permutations with Brooms. Algorithms, 15.","DOI":"10.3390\/a15070220"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"107448","DOI":"10.1016\/j.ress.2021.107448","article-title":"Novel Binary-Addition Tree Algorithm (BAT) for Binary-State Network Reliability Problem","volume":"208","author":"Yeh","year":"2021","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1016\/j.camwa.2010.09.033","article-title":"A practical bounding algorithm for computing two-terminal reliability based on decomposition technique","volume":"61","author":"Niu","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Dhivyabharathi, G.V., and Kumaresan, S. (2016, January 22\u201323). A survey on duplicate record detection in real world data. Proceedings of the 2016 3rd International Conference on Advanced Computing and Communication Systems (ICACCS), Coimbatore, India.","DOI":"10.1109\/ICACCS.2016.7586397"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Dong, H., Ge, Y., Zhou, R., and Wang, H. (2024). An Improved Sorting Algorithm for Periodic PRI Signals Based on Congruence Transform. Symmetry, 16.","DOI":"10.3390\/sym16040398"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"110217","DOI":"10.1016\/j.ress.2024.110217","article-title":"An algorithm to generate all d-lower boundary points for a stochastic flow network using dynamic flow constraints","volume":"249","author":"Huang","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Forghani-elahabad, M., and Alsalami, O.M. (2023). Using a Node\u2013Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints. Mathematics, 11.","DOI":"10.3390\/math11244889"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"107947","DOI":"10.1016\/j.ress.2021.107947","article-title":"Computing the reliability of a stochastic distribution network subject to budget constraint","volume":"216","author":"Xu","year":"2021","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1016\/S0305-0548(01)00062-4","article-title":"Search for All d-Mincuts of a Limited-Flow Network","volume":"29","author":"Yeh","year":"2002","journal-title":"Comput. Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1109\/TR.2023.3244955","article-title":"Computing the Reliability of a Multistate Flow Network with Flow Loss Effect","volume":"72","author":"Niu","year":"2023","journal-title":"IEEE Trans. Reliab."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1109\/TII.2016.2620121","article-title":"TDMA Versus CSMA\/CA for Wireless Multihop Communications: A Stochastic Worst-Case Delay Analysis","volume":"13","author":"Wang","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Sosa-Holwerda, A., Park, O.-H., Albracht-Schulte, K., Niraula, S., Thompson, L., and Oldewage-Theron, W. (2024). The Role of Artificial Intelligence in Nutrition Research: A Scoping Review. Nutrients, 16.","DOI":"10.3390\/nu16132066"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Heinrich, M., Valeske, B., and Rabe, U. (2022). Efficient Detection of Defective Parts with Acoustic Resonance Testing Using Synthetic Training Data. Appl. Sci., 12.","DOI":"10.3390\/app12157648"},{"key":"ref_20","first-page":"55","article-title":"Island microgrid based on distributed photovoltaic generation","volume":"42","author":"Zhang","year":"2014","journal-title":"Power Syst. Prot. Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","article-title":"An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints","volume":"18","author":"Deb","year":"2013","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Narushynska, O., Teslyuk, V., Doroshenko, A., and Arzubov, M. (2024). Data Sorting Influence on Short Text Manual Labeling Quality for Hierarchical Classification. Big Data Cogn. Comput., 8.","DOI":"10.3390\/bdcc8040041"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Bure\u0161, V., Cabal, J., \u010cech, P., Mls, K., and Ponce, D. (2020). The Influence of Criteria Selection Method on Consistency of Pairwise Comparison. Mathematics, 8.","DOI":"10.3390\/math8122200"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Basheer Ahmed, M.I., Zaghdoud, R., Ahmed, M.S., Sendi, R., Alsharif, S., Alabdulkarim, J., Albin Saad, B.A., Alsabt, R., Rahman, A., and Krishnasamy, G. (2023). A Real-Time Computer Vision Based Approach to Detection and Classification of Traffic Incidents. Big Data Cogn. Comput., 7.","DOI":"10.3390\/bdcc7010022"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Krivulin, N., Prinkov, A., and Gladkikh, I. (2022). Using Pairwise Comparisons to Determine Consumer Preferences in Hotel Selection. Mathematics, 10.","DOI":"10.3390\/math10050730"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Huang, D.-H., Huang, C.-F., and Lin, Y.-K. (2019). Reliability Evaluation for a Stochastic Flow Network Based on Upper and Lower Boundary Vectors. Mathematics, 7.","DOI":"10.3390\/math7111115"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Dodevska, Z., Radovanovi\u0107, S., Petrovi\u0107, A., and Deliba\u0161i\u0107, B. (2023). When Fairness Meets Consistency in AHP Pairwise Comparisons. Mathematics, 11.","DOI":"10.3390\/math11030604"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Cheon, J., Son, J., and Ahn, Y. (J. Ind. Eng. Chem., 2024). Economic and environmental factor-integrated optimal model for plastic-waste sorting, J. Ind. Eng. Chem., in press.","DOI":"10.1016\/j.jiec.2024.04.045"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"105453","DOI":"10.1016\/j.scs.2024.105453","article-title":"Large-scale EV charging scheduling considering on-site PV generation by combining an aggregated model and sorting-based methods","volume":"107","author":"Qian","year":"2024","journal-title":"Sustain. Cities Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111422","DOI":"10.1016\/j.est.2024.111422","article-title":"An enhanced sorting method for retired battery with feature selection and multiple clustering","volume":"87","author":"Liu","year":"2024","journal-title":"J. Energy Storage"},{"key":"ref_31","first-page":"12","article-title":"On Prime Numbers Generation and Pairing","volume":"3","year":"2023","journal-title":"Int. J. Innov. Res. Sci. Eng. Stud. (IJIRSES)"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s101070100263","article-title":"Benchmarking optimization software with performance profiles","volume":"91","author":"Dolan","year":"2002","journal-title":"Math. Program."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Ramamoorthy, J., Gupta, K., Shashidhar, N.K., and Varol, C. (2024). Linux IoT Malware Variant Classification Using Binary Lifting and Opcode Entropy. Electronics, 13.","DOI":"10.3390\/electronics13122381"},{"key":"ref_34","unstructured":"Brown, T.A. (2020). Gene Cloning and DNA Analysis: An Introduction, John Wiley & Sons."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Laforgia, A., Inchingolo, A.D., Piras, F., Colonna, V., Giorgio, R.V., Carone, C., Rapone, B., Malcangi, G., Inchingolo, A.M., and Inchingolo, F. (2024). Therapeutic Strategies and Genetic Implications for Periodontal Disease Management: A Systematic Review. Int. J. Mol. Sci., 25.","DOI":"10.3390\/ijms25137217"}],"container-title":["Big Data and Cognitive Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-2289\/8\/9\/96\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:42:31Z","timestamp":1760110951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-2289\/8\/9\/96"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,23]]},"references-count":35,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,9]]}},"alternative-id":["bdcc8090096"],"URL":"https:\/\/doi.org\/10.3390\/bdcc8090096","relation":{},"ISSN":["2504-2289"],"issn-type":[{"value":"2504-2289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,23]]}}}