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

2025/05/02 by Fatemeh Mohammadi, Mohammadi, Fatemeh, Eduardo Sáenz‐de‐Cabezón +3
Engineering · #Advanced Optical Network Technologies #Commutative Algebra (math.AC) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2505.01416

openalex publication_date 2025/05/02 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

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.

Citations

• Lcm-lattice, Taylor Bases and Minimal Free Resolutions of a Monomial ideal
• An Efficient Algorithm for Computing Network Reliability in Small\n Treewidth
• Efficient multicut enumeration of k-out-of-n:F and consecutive\n k-out-of-n:F systems
• Random Monomial Ideals
• Types of signature analysis in reliability based on Hilbert series
• The algebraic method in tree percolation
• Minimal Resolutions of Dominant and Semidominant Ideals
• Divisors on graphs, orientations, syzygies, and system reliability
• Finite atomic lattices and resolutions of monomial ideals
• Trees, parking functions, syzygies, and deformations of monomial ideals

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