{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T00:17:24Z","timestamp":1769559444662,"version":"3.49.0"},"reference-count":38,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,3,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In previous experimental study with three-way-reversal and juggling sequence rotation algorithms, using 20,000,000 elements for type LONG in Java, the average execution times have been shown to be 49.66761ms and 246.4394ms, respectively. These results have revealed appreciable low performance in the juggling algorithm despite its proven optimality. However, the juggling algorithm has also exhibited efficiency with some offset ranges. Due to this pattern of the juggling algorithm, the current study is focused on investigating source of the inefficiency on the average performance. Samples were extracted from the previous experimental data, presented differently and analyzed both graphically and in tabular form. Greatest common divisor values from the data that equal offsets were used. As emanating from the previous study, the Java language used for the rotation was to simulate ordering of tasks for safety and efficiency in the context of real-time task scheduling. Outcome of the investigation shows that juggling rotation performance competes favorably with three-way-reversal rotation (and even better in few cases) for certain offsets, but poorly with the rests. This study identifies the poorest performances around offsets in the neighborhood of<jats:italic>square root<\/jats:italic>of the sequence size. From the outcome, the study therefore strongly advises application developers (especially for real-time systems) to be mindful of<jats:italic>where<\/jats:italic>and<jats:italic>how<\/jats:italic>to in using juggling rotation.<\/jats:p>","DOI":"10.1515\/comp-2022-0234","type":"journal-article","created":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T00:56:23Z","timestamp":1647651383000},"page":"92-102","source":"Crossref","is-referenced-by-count":3,"title":["Greatest-common-divisor dependency of juggling sequence rotation efficient performance"],"prefix":"10.1515","volume":"12","author":[{"given":"Joseph A.","family":"Erho","sequence":"first","affiliation":[{"name":"Computer Science Department, Niger Delta University, Wilberforce Island , P.M.B. 071 , Amassoma , Bayelsa , Nigeria"}]},{"given":"Juliana I.","family":"Consul","sequence":"additional","affiliation":[{"name":"Mathematics Department, Niger Delta University, Wilberforce Island , P.M.B. 071 , Amassoma , Bayelsa , Nigeria"}]},{"given":"Bunakiye R.","family":"Japheth","sequence":"additional","affiliation":[{"name":"Computer Science Department, Niger Delta University, Wilberforce Island , P.M.B. 071 , Amassoma , Bayelsa , Nigeria"}]}],"member":"374","published-online":{"date-parts":[[2022,3,15]]},"reference":[{"key":"2022081707553236030_j_comp-2022-0234_ref_001","doi-asserted-by":"crossref","unstructured":"B. C. Huang and M. A. Langston, \u201cPractical in-place merging,\u201d Communications of the ACM, vol. 31, pp. 348\u2013352, 1988. 10.1145\/42392.42403.","DOI":"10.1145\/42392.42403"},{"key":"2022081707553236030_j_comp-2022-0234_ref_002","doi-asserted-by":"crossref","unstructured":"X. Wang, Y. Wub, and D. Zhua, \u201cA new variant of in-place sort algorithm,\u201d in: Proceedings of the International Workshop on Information and Electronics Engineering IWIEE (10\u201311 March 2012, Harbin, Heilongjiang), Elsevier, China, 2012, pp. 2274\u20132278, 10.1016\/j.proeng.2012.01.300.","DOI":"10.1016\/j.proeng.2012.01.300"},{"key":"2022081707553236030_j_comp-2022-0234_ref_003","unstructured":"A. A. Stepanov and D. E. Rose, From mathematics to generic programming, Pearson Education Inc, USA, 2015."},{"key":"2022081707553236030_j_comp-2022-0234_ref_004","unstructured":"J. Bentley, Programming pearls, 2nd edition, ACM Press\/Addison-Wesley Inc, USA, 2000."},{"key":"2022081707553236030_j_comp-2022-0234_ref_005","unstructured":"D. Gries and H. Mills, Swapping sections, Technical report 452, Cornell University, USA, 1981."},{"key":"2022081707553236030_j_comp-2022-0234_ref_006","doi-asserted-by":"crossref","unstructured":"I. Marouf, M. M. Asad, and Q. A. Al-Haija, \u201cReviewing and analyzing efficient GCD\/LCM algorithms for cryptographic design,\u201d Int. J. New Comput. Architectures Applicat. (IJNCAA), vol. 7, pp. 1\u20137, 2017, 10.17781\/P002301.","DOI":"10.17781\/P002301"},{"key":"2022081707553236030_j_comp-2022-0234_ref_007","unstructured":"A. A. Tamimi and A. M. Abdalla, \u201cA variable circular-shift image-encryption algorithm,\u201d in: H. R. Arabnia, L. Deligiannidi, F. G. Tinetti, Eds, 21st International Conference on Image Processing, Computer Vision, and Pattern Recognition (17\u201320 July 2017, Las Vegas, Nevada), USA, 2017, pp. 33\u201337."},{"key":"2022081707553236030_j_comp-2022-0234_ref_008","doi-asserted-by":"crossref","unstructured":"A. Fathy, I. F. Tarrad, H. F. A. Hamed, and A. I. Awad, \u201cAdvanced encryption standard algorithm: issues and implementation aspects,\u201d in: Proceedings of Advanced Machine Learning Technologies and Applications AMLTA 2012 Conference, Communications in Computer and Information Science, (8-10 December 2012, Cairo, Egypt), A. E. Hassanien, A. B. M. Salem, R. Ramadan, T. Kim, Eds, vol. 322, Springer, Berlin, Heidelberg, 2012, pp. 516\u2013523.","DOI":"10.1007\/978-3-642-35326-0_51"},{"key":"2022081707553236030_j_comp-2022-0234_ref_009","doi-asserted-by":"crossref","unstructured":"S. Baruah, \u201cFeasibility analysis of preemptive real-time systems upon heterogeneous multiprocessor platforms,\u201d in: 25th IEEE International Real-Time Systems Symposium,(5\u20138 December 2004, Lisbon, Portugal), IEEE, Portugal, 2004, pp. 37\u201346.","DOI":"10.1109\/REAL.2004.20"},{"key":"2022081707553236030_j_comp-2022-0234_ref_010","doi-asserted-by":"crossref","unstructured":"C. K. Shene, \u201cAn analysis of two in-place array rotation algorithms,\u201d Comput. J., vol. 40, pp. 541\u2013546, 1997.","DOI":"10.1093\/comjnl\/40.9.541"},{"key":"2022081707553236030_j_comp-2022-0234_ref_011","unstructured":"ISO\/IEC JTC1 SC22 WG21 N3690:2013, Programming languages, their environments and system software interfaces - C++, ISO, Geneva, Switzerland, 2013, pp. 978\u2013979."},{"key":"2022081707553236030_j_comp-2022-0234_ref_012","doi-asserted-by":"crossref","unstructured":"M. H. Weik, Circular Shift, Springer, US, Boston, MA, 2001, pp. 210\u2013210. 10.1007\/1-4020-0613-6_2654.","DOI":"10.1007\/1-4020-0613-6_2654"},{"key":"2022081707553236030_j_comp-2022-0234_ref_013","doi-asserted-by":"crossref","unstructured":"J. A. Erho, J. I. Consul, and B. R. Japheth. \u201cJuggling versus three-way-reversal sequence rotation performance across four data types,\u201d Int. J. Sci. Res. Comput. Sci. Eng., vol. 7, pp. 10\u201318, 2019.","DOI":"10.26438\/ijsrcse\/v7i6.1018"},{"key":"2022081707553236030_j_comp-2022-0234_ref_014","unstructured":"T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 3rd edition, MIT Press, London, England, 2009."},{"key":"2022081707553236030_j_comp-2022-0234_ref_015","doi-asserted-by":"crossref","unstructured":"C. Y. Huang, C. Y. Lai, and K. T. Cheng, \u201cFundamentals of algorithms,\u201d in: Electronic Design Automation: Synthesis, Verification, and Test, chapter 4, Morgan Kaufmann, L. T. Wang, Y. W. Chang, and K. T. Cheng, Eds., Elsevier, USA, 2009, pp. 173\u2013177.","DOI":"10.1016\/B978-0-12-374364-0.50011-4"},{"key":"2022081707553236030_j_comp-2022-0234_ref_016","unstructured":"H. S. Wilf, Algorithms and Complexity, 1st edition, Prentice Hall, U.S.A., 1994."},{"key":"2022081707553236030_j_comp-2022-0234_ref_017","unstructured":"D. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications Inc., Mineola, New York, 1998."},{"key":"2022081707553236030_j_comp-2022-0234_ref_018","doi-asserted-by":"crossref","unstructured":"P. S. Kim and A. Kutzner, \u201cRatio based stable in-place merging,\u201d in: M. Agrawal, D. Z. Du, Z. Duan, and A. Li, Eds., Proceedings of 5th International Conference on Theory and Applications of Models of Computation (25\u201329 April 2008, Xi\u2019an, China), Springer, China, 2008, pp. 246\u2013257. 10.1007\/978-3-540-79228-4_22.","DOI":"10.1007\/978-3-540-79228-4_22"},{"key":"2022081707553236030_j_comp-2022-0234_ref_019","doi-asserted-by":"crossref","unstructured":"K. Dudzinski and A. Dydek, \u201cOn a stable minimum storage merging algorithm,\u201d Inform. Process. Lett., vol. 12, pp. 5\u20138, 1981. 10.1016\/0020-0190(81)90065-X.","DOI":"10.1016\/0020-0190(81)90065-X"},{"key":"2022081707553236030_j_comp-2022-0234_ref_020","unstructured":"J. L. Hennessy and D. A. Patterson, Computer Architecture: A Quantitative Approach, 6th edition, Morgan Kaufmann publications, Elsevier, USA, 2019."},{"key":"2022081707553236030_j_comp-2022-0234_ref_021","doi-asserted-by":"crossref","unstructured":"J. Ramanujam, J. Hong, M. Kandemir, A. Narayan, and A. Agarwal, \u201cEstimating and reducing the memory requirements of signal processing codes for embedded systems,\u201d IEEE Trans Signal Process, vol. 54, pp. 286\u2013294, 2005.","DOI":"10.1109\/TSP.2005.855086"},{"key":"2022081707553236030_j_comp-2022-0234_ref_022","unstructured":"T. Yemliha, \u201cPerformance and memory space optimizations for embedded systems,\u201d Ph.D. thesis, Electrical Engineering and Computer Science \u2013 Dissertations. 300, Syracuse University, 2011. https:\/\/surface.syr.edu\/eecs_etd\/300 (Online; accessed, Jan 14, 2021)."},{"key":"2022081707553236030_j_comp-2022-0234_ref_023","doi-asserted-by":"crossref","unstructured":"P. R. Panda, F. Catthoor, N. D. Dutt, K. Danckaert, E. Brockmeyer, C. Kulkarni, et al., \u201cData and memory optimization techniques for embedded systems,\u201d ACM Trans. Design Automat. Electronic Syst., vol. 6, pp. 149\u2013206, 2001.","DOI":"10.1145\/375977.375978"},{"key":"2022081707553236030_j_comp-2022-0234_ref_024","unstructured":"A. R. Mahajan and M. S. Ali, \u201cOptimization of memory system in real-time embedded systems,\u201d in: Proceedings of 11th World Scientific and Engineering Academy and Society(WSEAS) International Conference on COMPUTERS (23\u201325 July 2007, Agios Nikolaos, Crete Island), N. E. Mastorakis, S. Kartalopoulos, D. Simian, A. Varonides, V. Mladenov, Z. Bojkovic, et al., Eds., Agios Nikolaos, Crete Island, Greece, 2007, pp. 13\u201319."},{"key":"2022081707553236030_j_comp-2022-0234_ref_025","unstructured":"A. Burns and A. Wellings, Real-time systems and programming languages: Ada 95, real-time java and real-time POSIX, 3rd edition, Pearson Education Limited, USA, 2001."},{"key":"2022081707553236030_j_comp-2022-0234_ref_026","doi-asserted-by":"crossref","unstructured":"W. Zhang, E. Bai, H. He, and A. M. K. Cheng, \u201cSolving energy-aware real-time tasks scheduling problem with shuffled frog leaping algorithm on heterogeneous platforms,\u201d Sensors, vol. 15, pp. 13778\u201313804, 2015.","DOI":"10.3390\/s150613778"},{"key":"2022081707553236030_j_comp-2022-0234_ref_027","doi-asserted-by":"crossref","unstructured":"X. Lin, Y. Lu, J. S. Deogun, and S. Goddard, \u201cReal-time divisible load scheduling for cluster computing,\u201d in: Proceedings of the 13th IEEE Real-Time and Embedded Technology and Applications Symposium, (3\u20136 April 2007, Bellevue, Washington), IEEE, USA, 2007, pp. 303\u2013314.","DOI":"10.1109\/RTAS.2007.29"},{"key":"2022081707553236030_j_comp-2022-0234_ref_028","unstructured":"S. N. Dinh, \u201cToward efficient scheduling for parallel real-time tasks on multiprocessors,\u201d PhD Thesis, Engineering and Applied Science Theses and Dissertations, Washington University, St. Louis, Missouri, 2020."},{"key":"2022081707553236030_j_comp-2022-0234_ref_029","unstructured":"D. C. Marinescu, Cloud Computing Theory and Practice, 1st edition, Morgan Kaufmann, Elsevier, USA, 2013."},{"key":"2022081707553236030_j_comp-2022-0234_ref_030","doi-asserted-by":"crossref","unstructured":"D. Mittermair and P. Puschner, \u201cWhich sorting algorithms to choose for hard real-time applications,\u201d in: Proceedings Ninth Euromicro Workshop on Real Time Systems, (11\u201313 June 1997, Toledo, Spain), Los Alamitos, CA, USA, 1997, 250\u2013257. 10.1109\/EMWRTS.1997.613792.","DOI":"10.1109\/EMWRTS.1997.613792"},{"key":"2022081707553236030_j_comp-2022-0234_ref_031","doi-asserted-by":"crossref","unstructured":"P. A. Laplante, Real-time Systems Design and Analysis, IEEE Press, Piscataway, NJ, 2004.","DOI":"10.1002\/0471648299"},{"key":"2022081707553236030_j_comp-2022-0234_ref_032","unstructured":"C. A. Furia, Rotation of sequences: algorithms and proofs, Technical report, Cornell University, USA, 2015."},{"key":"2022081707553236030_j_comp-2022-0234_ref_033","unstructured":"J. Bentley, \u201cCode from programming pearls,\u201d in: Programming Pearls, P. Gordon, ed., 2nd edition, chapter \u2018Column 2\u2019, ACM Press\/Addison-Wesley Inc, USA, 2000, pp. 140\u2013143."},{"key":"2022081707553236030_j_comp-2022-0234_ref_034","doi-asserted-by":"crossref","unstructured":"A. Symvonis, \u201cOptimal stable merging,\u201d Comput. J., vol. 38, pp. 681\u2013690, 1995, 10.1093\/comjnl\/38.8.681.","DOI":"10.1093\/comjnl\/38.8.681"},{"key":"2022081707553236030_j_comp-2022-0234_ref_035","unstructured":"J. A. Erho and J. I. Consul, \u201cPrecise evaluation of execution cost of sequence rotation by three-way-reversals,\u201d Int. J. Appl. Sci. Res., vol. 2, pp. 99\u2013104, 2019."},{"key":"2022081707553236030_j_comp-2022-0234_ref_036","unstructured":"H. G. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th edition, Oxford University Press, London, 1979."},{"key":"2022081707553236030_j_comp-2022-0234_ref_037","unstructured":"J. A. Erho, B. R. Japheth, E. F. Osaisai, and J. I. Consul, \u201cPoor performance of juggling sequence rotation as greatest-common-divisor dependent,\u201d in: Lecture Notes in Engineering and Computer Science: Proceedings of The International MultiConference of Engineers and Computer Scientists 2021, (20\u201322 October, 2021, Hong Kong), IAENG, China, 2021, pp. 70\u201374."},{"key":"2022081707553236030_j_comp-2022-0234_ref_038","doi-asserted-by":"crossref","unstructured":"B. Gastel and R. A. Day, How to Write and Publish a Scientific Paper, 8th edition, Greenwood ABC-CLIO, LLC, United States of America, 2016.","DOI":"10.5040\/9798400666926"}],"container-title":["Open Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2022-0234\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2022-0234\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T15:57:06Z","timestamp":1726847826000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/comp-2022-0234\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,1]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,3,16]]},"published-print":{"date-parts":[[2022,3,16]]}},"alternative-id":["10.1515\/comp-2022-0234"],"URL":"https:\/\/doi.org\/10.1515\/comp-2022-0234","relation":{},"ISSN":["2299-1093"],"issn-type":[{"value":"2299-1093","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,1]]}}}