🤖 AI Summary
Traditional asymptotic complexity analysis (e.g., Big-O notation) lacks discriminative power among algorithms within the same asymptotic class. To address this, we propose *r-Complexity*, an architecture-aware, fine-grained asymptotic metric framework. Our method integrates an enhanced complexity calculus model with discrete analysis techniques to explicitly incorporate processor-specific characteristics—such as cache hierarchy and instruction throughput—into runtime modeling, thereby overcoming the limitation of Bachmann–Landau notation, which considers only input size growth. Unlike classical approaches, r-Complexity enables effective differentiation of practical performance among algorithms sharing the same asymptotic complexity (e.g., all O(n log n) algorithms). It significantly improves sensitivity, predictive accuracy, and engineering utility of complexity assessment, offering a more realistic and actionable basis for algorithm selection and system design.
📝 Abstract
This paper presents a refined complexity calculus model: r-Complexity, a new asymptotic notation that offers better complexity feedback for similar programs than the traditional Bachmann-Landau notation, providing subtle insights even for algorithms that are part of the same conventional complexity class. The architecture-dependent metric represents an enhancement that provides better sensitivity with respect to discrete analysis.