{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:45:37Z","timestamp":1760147137794,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T00:00:00Z","timestamp":1673222400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100015690","name":"Riset Kompetensi Dosen Unpad (RKDU)","doi-asserted-by":"publisher","award":["2203\/UN6.3.1\/PT.00\/2022"],"award-info":[{"award-number":["2203\/UN6.3.1\/PT.00\/2022"]}],"id":[{"id":"10.13039\/501100015690","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In max-plus algebra, some algorithms for determining the eigenvector of irreducible matrices are the power algorithm and the Kleene star algorithm. In this research, a modified Kleene star algorithm will be discussed to compensate for the disadvantages of the Kleene star algorithm. The Kleene star algorithm\u2019s time complexity is O(n(n!)), and the new Kleene star algorithm\u2019s time complexity is O(n4), while the power algorithm\u2019s time complexity cannot be calculated. This research also applies max-plus algebra in a railroad network scheduling problem, constructing a graphical user interface to perform schedule calculations quickly and easily.<\/jats:p>","DOI":"10.3390\/computation11010011","type":"journal-article","created":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T01:30:47Z","timestamp":1673314247000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modified Kleene Star Algorithm Using Max-Plus Algebra and Its Application in the Railroad Scheduling Graphical User Interface"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1794-7252","authenticated-orcid":false,"given":"Ema","family":"Carnia","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rinaldi","family":"Wilopo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1638-282X","authenticated-orcid":false,"given":"Herlina","family":"Napitupulu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nursanti","family":"Anggriani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0129-6344","authenticated-orcid":false,"given":"Asep K.","family":"Supriatna","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,9]]},"reference":[{"key":"ref_1","unstructured":"Farlow, K.G. (2009). Max-Plus Algebra, Virginia Polytechnic Institute and State University."},{"key":"ref_2","unstructured":"Krivulin, N.K. (2012, December 01). The Max-Plus Algebra Approach in Modelling of Queueing Networks. Available online: http:\/\/arxiv.org\/abs\/1212.0895."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1016\/S1474-6670(17)42064-7","article-title":"On Large Scale Max-Plus Algebra Models in Railway Systems","volume":"31","author":"Olsder","year":"1998","journal-title":"IFAC Proc. Vol."},{"key":"ref_4","unstructured":"Elmahi, I., Grunder, O., and Elmoudni, A. (2003, January 23\u201325). A Max Plus Algebra Approach for Modelling and Control a Supply Chain. Proceedings of the 2003 IEEE Conference on Control Applications, Istanbul, Turkey."},{"key":"ref_5","unstructured":"Imaev, A., and Judd, R.P. (2009, January 10\u201312). Block diagram-based modeling of manufacturing systems using. Proceedings of the 2009 American Control Conference, St. Louis, MO, USA."},{"key":"ref_6","unstructured":"Becker, B.A., and Lastovetsky, A. (2010, January 13\u201316). Max-Plus Algebra and Discrete Event Simulation on Parallel Hierarchical Heterogeneous Platforms. Proceedings of the 2010 Conference on Parallel Processing, San Diego, CA, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01805562","article-title":"Eigenvalues of dynamic max-min systems","volume":"1","author":"Olsder","year":"1991","journal-title":"Discret. Event Dyn. Syst. Theory Appl."},{"key":"ref_8","unstructured":"Braker, J.G. (1993). Algorithms and Applications in Timed Discrete Event Systems, Delft University of Technology."},{"key":"ref_9","unstructured":"(2021, December 01). Aljabar Min-Max Plus dan Terapannya. Available online: https:\/\/docplayer.info\/68251215-Aljabar-min-max-plus-dan-terapannya.html."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s10626-016-0235-4","article-title":"On a generalization of power algorithms over max-plus algebra","volume":"27","author":"Fahim","year":"2017","journal-title":"Discret. Event Dyn. Syst."},{"key":"ref_11","unstructured":"Baccelli, F., Cohen, G., Olsder, G.J., and Quadrat, J.-P. (1992). Quadrat, Synchronization and Linearity: An Algebra for Discrete Event Systems, John Wiley & Sons."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00778-012-0286-6","article-title":"OXPath: A language for scalable data extraction, automation, and crawling on the deep web","volume":"22","author":"Furche","year":"2013","journal-title":"VLDB J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"012019","DOI":"10.1088\/1757-899X\/332\/1\/012019","article-title":"Eigenvectors determination of the ribosome dynamics model during mRNA translation using the Kleene Star algorithm","volume":"332","author":"Ernawati","year":"2018","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s10287-020-00374-5","article-title":"Tropical optimization technique in bi-objective project scheduling under temporal constraints","volume":"17","author":"Krivulin","year":"2020","journal-title":"Comput. Manag. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/s10626-019-00304-x","article-title":"Modelling and control of periodic time-variant event graphs in dioids","volume":"30","author":"Trunk","year":"2020","journal-title":"Discret. Event Dyn. Syst."},{"key":"ref_16","unstructured":"Rudhito, M.A. (2016). Aljabar Max-Plus Dan Penerapannya, Sanata Dharma University Press."},{"key":"ref_17","first-page":"189","article-title":"Nilai Eigen Dan Vektor Eigen Matriks Atas Aljabar Max-Plus","volume":"6","author":"Tunisa","year":"2017","journal-title":"UJM"},{"key":"ref_18","unstructured":"Alfiah, S. (2011). Pemodelan Jaringan Kereta Rel Listrik (KRL) Menggunakan Aljabar Max-Plu. [Master\u2019s Thesis, Institut Teknologi Sepuluh Nopember]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1137\/0204007","article-title":"Finding All the Elementary Circuits of a Directed Graph","volume":"4","author":"Johnson","year":"1975","journal-title":"SIAM J. 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