Journal: Volume 31, No. 2, 2026
Pages: 85 – 96
DOI: https://doi.org/10.62660/bcstu/2.2026.85
239 Views

Application of linear algebra methods for optimising data processing and storage in modern information systems

Olexandr Kraychuk, Serhii Kraychuk, Nataliia Ostapchuk
Received 29.12.2025
Revised 25.03.2026
Accepted 18.05.2026
Published 26.06.2026

Abstract

The aim of the study was to generalise approaches to coordinating decisions at the stages of planning, execution, and physical level of data representation in information systems under the dominance of resource constraints when operating with massive sets. The methodology was based on system-analytical formalisation, comparative-analytical generalisation and typology, comparative analysis, systematisation and integrative synthesis. It was established that linear algebra formalises the representation of data as matrices/vectors and calculations as a sequence of transformations. The generalisation of operations (semirings) extends these primitives to graph and Boolean problems, and Graph Basic Linear Algebra Subprograms standardises the implementation for sparse structures. Efficiency is determined by the consistent chain of “rewrite→cost model→physical execution”: rewrite reduces intermediate data, and the cost model chooses a plan based on data input/output, memory, sparsity, and parallelism, without it, heuristics remain. Factorised representations have been found to reduce redundancy and pressure on memory and data input/output (for joins/groups) with system support. Randomised Numerical Linear Algebra and sketching reduce costs and manage the “accuracy-resources” trade-off in streaming processing. Matrix compression (low-rank representation, reduced precision) reduces memory and traffic and speeds up computations with a controlled loss of precision. In vector database management systems and distributed systems, the bottleneck is data input/output and redistribution between nodes, so DShuffle moves some processing closer to the data, emphasising the role of infrastructure optimisation. The linear algebraic representation of computations provides a basis for consistent optimisation of rewriting, plan selection, and execution, reducing materialisation and data movement under input/output, memory, and bandwidth constraints. The practical significance of the results lies in the possibility of the application by information-systems developers and engineers for the consistent selection of data formats, execution plans, and computational primitives to reduce materialisation and I/O, memory, and network overhead

Keywords

operations; matrices; resource constraints; sparsity; materialisation; databases

References

  1. Ahfock, D., Astle, W.J., & Richardson, S. (2023). On randomized sketching algorithms and the Tracy-Widom law. Statistics and Computing, 33, article number 34. doi: 10.1007/s11222-022-10148-5.
  2. Bao, X., et al. (2024). Rock: Cleaning data by embedding ML in logic rules. In Companion of the 2024 international conference on management of data (pp. 106-119). New York: Association for Computing Machinery. doi: 10.1145/3626246.3653372.
  3. Boehm, M., Interlandi, M., & Jermaine, C. (2023). Optimizing tensor computations: From applications to compilation and runtime techniques. In Companion of the 2023 international conference on management of data (pp. 53-59). New York: Association for Computing Machinery. doi: 10.1145/3555041.358940.
  4. Brock, B., Buluç, A., Mattson, T.G., McMillan, S., & Moreira, J. (2021). The GraphBLAS C API specification: Version 2.0.0. Retrieved from https://graphblas.org/docs/GraphBLAS_API_C_v2.0.0.pdf.
  5. Ding, B., Narasayya, V., & Chaudhuri, S. (2024). Extensible query optimizers in practice. Foundations and Trends in Databases, 14(3-4), 186-402. doi: 10.1561/1900000077.
  6. Ding, C., Li, S., Lu, K., Yao, T., Wang, D., Wu, H., Wan, J., Tan, Z., & Xie, C. (2025). DShuffle: DPU-optimized shuffle framework for large-scale data processing. In 2025 USENIX annual technical conference (pp. 1371-1386). Boston: USENIX Association.
  7. Geerts, F., Muñoz, T., Riveros, C., & Vrgoč, D. (2021). Expressive power of linear algebra query languages. In Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI symposium on principles of database systems (pp. 342-354). New York: Association for Computing Machinery. doi: 10.1145/3452021.3458314.
  8. GraphBLAS Forum. (n.d.). Retrieved from https://graphblas.org/.
  9. Hordiichuk-Bublivska, O.V., & Fabri, L.P. (2022). Matrix factorization of big data in the industrial systems. Ukrainian Journal of Information Technology, 4(2), 68-73. doi: 10.23939/ujit2022.02.068.
  10. Hsu, Y.-C., Hua, T., Chang, S.-E., Lou, Q., Shen, Y., & Jin, H. (2022). Language model compression with weighted low-rank factorization. ArXiv. doi: 10.48550/arXiv.2207.00112.
  11. Jin, G., Bian, H., Chen, Y., & Du, X. (2022). Columnar storage optimization and caching for data lakes. In Proceedings of the 25th international conference on extending database technology (pp. 419-423). Edinburgh: Open Proceedings. doi: 10.48786/edbt.2022.33.
  12. Kwon, T., Ko, J., Jung, J., Jang, J.-G., & Shin, K. (2025). Compact lossy compression of tensors via neural tensor-train decomposition. Knowledge and Information Systems, 67, 1169-1211. doi: 10.1007/s10115024-02252-x.
  13. Lane, P.A., & Booth, J.D. (2023). Heterogeneous sparse matrix-vector multiplication via compressed sparse row format. Parallel Computing, 115, article number 102997. doi: 10.1016/j.parco.2023.102997.
  14. Li, Z., Sun, W., Zhan, D., Kang, Y., Chen, L., Bozzon, A., & Hai, R. (2024). Amalur: The convergence of data integration and machine learning. IEEE Transactions on Knowledge and Data Engineering, 36(12), 7353-7367. doi: 10.1109/ TKDE.2024.3357389.
  15. Liu, C., Pavlenko, A., Interlandi, M., & Haynes, B. (2025). Data formats in analytical DBMSs: Performance tradeoffs and future directions. The VLDB Journal, 34, article number 30. doi: 10.1007/s00778-025-00911-1.
  16. Marichal, R., Dufrechou, E., & Ezzatti, P. (2021). Optimizing sparse matrix storage for the big data era. In M. Naiouf, E. Rucci, F. Chichizola & L. De Giusti (Eds.), 9th conference: Cloud computing, big data & emerging topics (pp. 121-135). Cham: Springer. doi: 10.1007/978-3-030-84825-5_9.
  17. Mastoras, A., Anagnostidis, S., & Yzelman, A.-J.N. (2023). Design and implementation for nonblocking execution in GraphBLAS: Tradeoffs and performance. ACM Transactions on Architecture and Code Optimization, 20(1), article number 6. doi: 10.1145/3561652.
  18. Muñoz, T. (2025). Enumeration-based dynamic query processing for linear algebra workloads in data science. In VLDB 2025: PhD workshop. London: QEII Centre.
  19. Olteanu, D. (2023). Report on the workshop on factorized databases. SIGMOD Record, 52(2), 53-56.
  20. Pan, J.J., Wang, J., & Li, G. (2024). Survey of vector database management systems. The VLDB Journal, 33, 15911615. doi: 10.1007/s00778-024-00864-x.
  21. Pan, Y., Sun, J., & Yu, H. (2023). LM-DiskANN: Low memory footprint in disk-native dynamic graph-based ANN indexing. In 2023 IEEE international conference on big data (pp. 5987-5996). Sorrento: IEEE. doi: 10.1109/ BigData59044.2023.10386517.
  22. Ren, Z., Doekemeijer, K., Apparao, P., & Trivedi, A. (2025). Storage-based approximate nearest neighbor search: What are the performance, cost, and I/O characteristics? In 2025 IEEE international symposium on workload characterization (pp. 407-422). Irvine: IEEE. doi: 10.1109/IISWC66894.2025.00041.
  23. Saha, R., Srivastava, V., & Pilanci, M. (2023). Matrix compression via randomized low rank and low precision factorization. In Proceedings of the 37th international conference on neural information processing systems (pp. 18828-18872). Red Hook: Curran Associates Inc.
  24. Serrano, T.M., Riveros, C., & Vansummeren, S. (2024). Enumeration and updates for conjunctive linear algebra queries through expressibility. In Proceedings of the 27th international conference on database theory (ICDT 2024). Wadern: Dagstuhl Publishing. doi: 10.4230/LIPIcs.ICDT.2024.12.
  25. Shen, Z., Cai, Y., Cheng, K., Lee, P.P.C., Li, X., Hu, Y., & Shu, J. (2025). A survey of the past, present, and future of erasure coding for storage systems. ACM Transactions on Storage, 21(1), article number 4. doi: 10.1145/3708994.
  26. Striamets, S.P., & Opotyak, Yu.V. (2021). Matrix parallel processor based on a homogeneous computational medium using an advanced computing cell. Ukrainian Journal of Information Technology, 3(1), 78-84. doi: 10.23939/ujit2021.03.078.
  27. Sun, W., Katsifodimos, A., & Hai, R. (2025). Accelerating machine learning queries with linear algebra query processing. Distributed and Parallel Databases, 43, article number 8. doi: 10.1007/s10619-02407451-7.
  28. Tian, B., Liu, H., Duan, Z., Liao, X., Jin, H., & Zhang, Y. (2024). Scalable billion-point approximate nearest neighbor search using SmartSSDs. In Proceedings of the 2024 USENIX annual technical conference (pp. 1135-1150). San Francisco: USENIX Association.
  29. Udell, M., & Frangella, Z. (2023). Randomized numerical linear algebra for optimization. Retrieved from https:// web.stanford.edu/~udell/doc/udell2022_randnla4opt.pdf.
  30. Yin, H., Wen, D., Li, J., Wei, Z., Zhang, X., Huang, Z., & Li, F. (2024). Optimal matrix sketching over sliding Windows. Proceedings of the VLDB Endowment, 17(9), 2149-2161. doi: 10.14778/3665844.3665847.
  31. Zeng, X., Hui, Y., Shen, J., Pavlo, A., McKinney, W., & Zhang, H. (2023). An empirical evaluation of columnar storage formats. Proceedings of the VLDB Endowment, 17(2), 148-161. doi: 10.14778/3626292.3626298.
  32. Zhang, Z., Liu, F., Huang, G., Liu, X., & Jin, X. (2024). Fast vector query processing for large datasets beyond GPU memory with reordered pipelining. In Proceedings of the 21st USENIX symposium on networked systems design and implementation (pp. 23-40). Santa Clara: USENIX Association.

Suggested citation

Kraychuk, O., Kraychuk, S., & Ostapchuk, N. (2026). Application of linear algebra methods for optimising data processing and storage in modern information systems. Bulletin of Cherkasy State Technological University, 31(2), 85-96. https://doi.org/10.62660/bcstu/2.2026.85