METHODS OF NAVIGATING ALGORITHMIC COMPLEXITY: BIG-OH AND SMALL-OH NOTATIONS
DOI:
https://doi.org/10.37943/15DNLB5877Keywords:
Big-Oh notation, small-oh notation, algorithmic analysis, asymptotic analysisAbstract
This article provides an in-depth exploration of Big-Oh and small-oh notations, shedding light on their practical implications in the analysis of algorithm complexity. Big-Oh notation offers a valuable tool for estimating an upper bound on the growth rate of an algorithm's running time, whereas small-oh notation delineates a lower limit on this growth rate. The piece delves into a comprehensive examination of various complexity classes that emerge through the application of Big-Oh notation, underscoring the significance of small-oh notation as it complements and enriches complexity analysis.
In the realm of programming and computer science, the employment of these notations holds paramount importance. They empower developers and researchers to make informed decisions regarding algorithm selection and optimization. It is crucial to recognize that while complexity analysis is a vital facet of effective programming, ongoing research endeavors may yield more refined methodologies and approaches within this domain.
By understanding and harnessing the power of Big-Oh and small-oh notations, professionals can effectively evaluate algorithm efficiency and scalability. This knowledge equips them with the ability to design and implement algorithms that meet specific performance criteria, which is pivotal in the ever-evolving landscape of technology and computation. As pushing the boundaries of what is possible in the field of algorithm design is being continued, these notations remain invaluable tools for navigating the complex terrain of algorithmic analysis and optimization.
By embracing Big-Oh and small-oh notations, professionals can finely assess algorithmic efficiency, ensuring they meet performance criteria in the evolving technological landscape. These notations remain indispensable for algorithmic analysis.
References
Sipser, M. (2013). Introduction to the theory of computation (3rd ed.). Cengage Learning.
Shaffer, C. A. (2013). A practical introduction to data structures and algorithm analysis (3rd ed.). Prentice Hall.
Ericson, F. (2019). Algorithms. Pearson Education.
Sedgewick, R., & Flajolet, P. (2013). An introduction to the analysis of algorithms (2nd ed.). Addison-Wesley Professional.
Kleinberg, J., & Tardos, É. (2022). Algorithm design (2nd ed.). Pearson Education.
Chakraborty, P., Khatoon, R., & Dutta, S. (2019). A guide to design and analysis of algorithms. CRC Press.
Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. (2022). Introduction to algorithms (4th ed.). MIT Press.
Muller, S., & Massaron, L. (2017). Algorithms for dummies. John Wiley & Sons.
Lee, C.-H., Tseng, H.-Y., Chang, Y.-H., & Tsai, W.-T. (2017). Introduction to the design and analysis of algorithms: A strategic approach. CRC Press.
Skiena, S. S. (2020). The algorithm design manual, 3rd edition. Springer.
Lafore, R. (2014). Data structures and algorithms in Java, 6th edition. Pearson.
Chistikov, D., Kiefer, S., Murawski, A. S., & Purser, D. (2020). The Big-O Problem for Labelled Markov Chains and Weighted Automata. Leibniz International Proceedings in Informatics, 166, 1-19. https://doi.org/10.4230/LIPIcs.CONCUR.2020.41.
Bouyer, P., Markey, N., & Ouaknine, J. (2019). The Big-O problem. Logical Methods in Computer Science, 15(3), 1-44. https://doi.org/10.23638/LMCS-15(3:1)2019.
Agarwal, P. K., Har-Peled, S., & Varadarajan, K. R. (2014). Approximate nearest neighbor for polygonal curves under Fréchet distance. Leibniz International Proceedings in Informatics (LIPIcs), 29-40. https://doi.org/10.4230/LIPIcs.STACS.2014.29
Pugliese, R., Regongdi, S., & Marini, R. (2021). Machine learning-based approach: global trends, research directions, and regulatory standpoints. Data Science and Management, 4, 19-29. https://doi.org/10.1016/j.dsm.2021.12.002.
Xu, Y., Liu, X., Cao, X., Huang, C., Liu, E., Qian, S., Liu, X., Wu, Y., Dong, F., Qiu, C.-W., Qiu, J., Hua, K., Su, W., Wu, J., Xu, H., Han, Y., Fu, C., Yin, Z., Liu, M., Roepman, R., & Zhang, J. (2021). Artificial intelligence: A powerful paradigm for scientific research. The Innovation, 2(4), 100179. https://doi.org/10.1016/j.xinn.2021.100179.
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