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

TL;DR

This paper introduces the lcm-filtration and stepwise filtration methods for analyzing redundancy in networks and systems, focusing on computational efficiency and effectiveness in various scenarios.

Contribution

It proposes a novel stepwise filtration approach that reduces unnecessary computations compared to traditional lcm-filtration, improving analysis of networks and system signatures.

Findings

Stepwise filtration outperforms lcm-filtration in efficiency.

The methods effectively analyze network redundancy and system signatures.

Stepwise filtration reduces computational complexity in practical applications.

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.