Multi-Metric Algorithmic Complexity: Beyond Asymptotic Analysis

TL;DR

This paper introduces a weighted-operation complexity model that evaluates algorithms across multiple dimensions like time, energy, and cost, providing a practical tool for architecture-aware analysis beyond traditional asymptotic methods.

Contribution

It presents a novel multi-metric complexity model that assigns realistic costs to operations, enabling comprehensive, multi-objective algorithm evaluation in real-world scenarios.

Findings

High correlation ( >0.9) with measured data across architectures

Outperforms traditional baselines like Big-O, ICE, and EVM gas

Provides practical efficiency recommendations for various algorithms

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 (\r{ho}>0.9) with measured data, outperforming baselines in multi-objective scenarios.