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.
@article{arxiv.2505.01416,
title = {Redundancy analysis using lcm-filtrations: networks, system signature and sensitivity evaluation},
author = {Fatemeh Mohammadi and Eduardo Sáenz-de-Cabezón and Henry Wynn},
journal= {arXiv preprint arXiv:2505.01416},
year = {2025}
}