Time Complexity in the Age of Big Data and Artificial Intelligence: A Multi-Dimensional Framework

This preprint presents a conceptual re-examination of time complexity in the context of modern Big Data and Artificial Intelligence systems. Classical asymptotic analysis, while foundational, assumes sequential execution and abstracts away system-level constraints that increasingly dominate real-world performance in large-scale, distributed, and energy-intensive workloads. The paper introduces a multi-dimensional framework for effective time complexity that integrates five interacting components: computational cost, communication overhead, memory and cache effects, energy consumption, and empirical performance metrics. Normalization coefficients are defined to map heterogeneous system metrics into a unified time-equivalent representation, enabling principled comparison between algorithms that are theoretically similar but system-wise divergent. Through symbolic formulations and lightweight simulations of distributed training and generative inference, the framework illustrates how communication and energy costs reshape practical efficiency in multi-GPU environments. The work is intended as an analytical and system-aware extension of classical complexity theory rather than a replacement, providing a foundation for scalability analysis, energy-aware algorithm design, and algorithm–hardware co-design in contemporary AI systems.