OPTIMIZING COMPUTATIONAL ALGORITHMS BASED ON SET THEORY AND MODERN DATA STRUCTURES
Keywords:
Set Theory, Data Structure, Computational Efficiency, Databases, Algorithms, Data Processing.Abstract
This article explores the issue of enhancing the efficiency of computational algorithms through the integration of set theory principles with modern data structures. The research analyzes the possibilities of applying set operations such as union, intersection, and difference to large-scale databases and analytical systems. Experimental results confirm the optimization of query processing and memory consumption using algorithms structured on set theory. The proposed method creates an effective link between theoretical mathematics and practical data systems, enabling increased computational performance in big data computing systems.
References
Cantor, G. (1890). To‘plamlar nazariyasining asoslari. Matematika jurnali.
Knuth, D. E. (1998). Ma'lumotlar strukturalari va algoritmlar. Addison-Wesley.
Stonebraker, M., & Hellerstein, J. M. (2005). SQL tizimlarida optimallashtirish. IEEE Data Engineering Bulletin.
Dean, J., & Ghemawat, S. (2008). Katta ma'lumotlarni qayta ishlash. Communications of the ACM.
Codd, E. F. (1970). Relatsion ma'lumotlar modeli. Communications of the ACM.
Maier, D. (1983). To‘plamlar nazariyasining ma'lumotlar bazalariga qo‘llanilishi. Morgan Kaufmann.
Horton, J., & Lachance, C. (2012). Tarqatilgan tizimlarda ma'lumotlar samaradorligini oshirish. Journal of Big Data.
