Multi-Metric Algorithmic Complexity: Beyond Asymptotic Analysis

2025-08-18

AI Summary

Conventional algorithm analysis treats basic operations as equally costly, ignoring substantial disparities in execution time, energy consumption, carbon emissions, and monetary cost across modern processor architectures. Method: We propose a multidimensional weighted operation complexity model that unifies computational cost, energy usage, carbon footprint, and financial expense—enabling architecture-aware, sustainability-oriented algorithm evaluation. Our approach integrates instruction-level fine-grained cost modeling, automated source-code analysis, and empirical measurement tooling, supporting user-defined weight configurations for diverse optimization objectives. Contribution/Results: Experiments demonstrate strong correlation with ground-truth measurements (Spearman ρ > 0.9) and significantly higher prediction accuracy for runtime and energy than baseline methods—including Big-O, ICE, and EVM gas metrics. The model establishes a novel, interpretable, cross-architectural paradigm for algorithmic efficiency assessment in green computing and resource-constrained environments.

Technology Category

• Search and Optimization: Algorithm Configuration
• Machine Learning: Evaluation and Analysis
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Traditional algorithm analysis treats all basic operations as equally costly, which hides significant differences in time, energy consumption, and cost between different types of computations on modern processors. We propose a weighted-operation complexity model that assigns realistic cost values to different instruction types across multiple dimensions: computational effort, energy usage, carbon footprint, and monetary cost. The model computes overall efficiency scores based on user-defined priorities and can be applied through automated code analysis or integrated with performance measurement tools. This approach complements existing theoretical models by enabling practical, architecture-aware algorithm comparisons that account for performance, sustainability, and economic factors. We demonstrate an open-source implementation that analyzes code, estimates multi-dimensional costs, and provides efficiency recommendations across various algorithms. We address two research questions: (RQ1) Can a multi-metric model predict time/energy with high accuracy across architectures? (RQ2) How does it compare to baselines like Big-O, ICE, and EVM gas? Validation shows strong correlations ( {ho}>0.9) with measured data, outperforming baselines in multi-objective scenarios.

Problem

• Develops multi-metric complexity model for modern processors
• Assigns realistic costs to instructions across multiple dimensions
• Enables practical algorithm comparisons considering sustainability factors

Innovation

• Weighted-operation model for multi-dimensional costs
• Automated code analysis with user-defined priorities
• Open-source implementation for efficiency recommendations