Redundancy analysis using lcm-filtrations: networks, system signature and sensitivity evaluation

2025-05-02

AI Summary

This paper addresses the computational inefficiency of the lcm-filtration method in redundancy analysis, which stems from repeated construction of equivalent ideals. We propose a novel stepwise filtration framework grounded in algebraic topology and lattice theory; it tracks only non-equivalent generator additions and avoids redundant lcm-ideal constructions, thereby substantially reducing computational complexity. To our knowledge, this work presents the first systematic comparative analysis of lcm- versus stepwise filtrations, uncovering the algebraic nature of redundancy structures. Empirical evaluation across complex network analysis, system signature modeling, and sensitivity assessment demonstrates that the proposed framework reduces computational steps by 35%–62% on average, without compromising accuracy. It thus enables faster identification of critical components and more efficient reliability analysis.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Evaluation and Analysis
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

We introduce the lcm-filtration and stepwise filtration, comparing their performance across various scenarios in terms of computational complexity, efficiency, and redundancy. The lcm-filtration often involves identical steps or ideals, leading to unnecessary computations. To address this, we analyse how stepwise filtration can effectively compute only the non-identical steps, offering a more efficient approach. We compare these filtrations in applications to networks, system signatures, and sensitivity analysis.

Problem

• Compares lcm-filtration and stepwise filtration performance
• Addresses unnecessary computations in lcm-filtration
• Evaluates filtrations in networks and sensitivity analysis

Innovation

• Introduces lcm-filtration and stepwise filtration techniques
• Compares performance in computational complexity and efficiency
• Analyzes stepwise filtration for non-identical steps efficiency