Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2110.13390

Novel Binary Addition Tree Algorithm (BAT) for Calculating the Direct Lower-Bound of the Highly Reliable Binary-State Network Reliability

Wei-Chang Yeh
View original source ↗Read source document ↗Export metadata ↓

Abstract

Real-world applications such as the internet of things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems are typically modeled as network structures. Network reliability represents the success probability of a network and it is an effective and popular metric for evaluating the performance of all types of networks. Binary-state networks composed of binary-state (e.g., working or failed) components (arcs and/or nodes) are some of the most popular network structures. The scale of networks has grown dramatically in recent years. For example, social networks have more than a billion users. Additionally, the reliability of components has increased as a result of both mature and emergent technology. For highly reliable networks, it is more practical to calculate approximated reliability, rather than exact reliability, which is an NP-hard problem. Therefore, we propose a novel direct reliability lower bound based on the binary addition tree algorithm to calculate approximate reliability. The efficiency and effectiveness of the proposed reliability bound are analyzed based on time complexity and validated through numerical experiments.

Explore related subjects

cs.DMcs.NIcs.SYeess.SYmath.COmath.PR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Wei-Chang Yeh. 2021-10-26. Novel Binary Addition Tree Algorithm (BAT) for Calculating the Direct Lower-Bound of the Highly Reliable Binary-State Network Reliability. https://arxiv.org/abs/2110.13390

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Flip Dynamics for Sampling Colorings: Improving $(11/6-ε)$ Using a Simple Metric

We present improved bounds for randomly sampling $k$-colorings of graphs with maximum degree $Δ$; our results hold without any further structural assumptions on the graph. The Glauber dynamics is a simple single-site update Markov chain. Jerrum (1995) proved an optimal $O(n\log{n})$ mixing-time bound for Glauber dynamics whenever $k>2Δ$ where $Δ$ is the maximum degree of the input graph. This bound was improved by Vigoda (1999) to $k>(11/6)Δ$ using a "flip" dynamics which recolors (small) maximal two-colored components in each step. Vigoda's result was the best known for general graphs for 20 years until Chen et al. (2019) established optimal mixing of the flip dynamics for $k>(11/6-\varepsilon)Δ$ where $\varepsilon\approx 10^{-5}$. We present the first substantial improvement over these results. We prove an optimal mixing-time bound of $O(n\log{n})$ for the flip dynamics when $Δ\geq125$ and $k\geq1.809Δ$. This yields, through recent spectral independence results, an optimal $O(n\log{n})$ mixing time for the Glauber dynamics for every fixed $Δ\geq125$ in the same range of $k/Δ$. Our proof utilizes path coupling with a simple weighted Hamming distance for "unblocked" neighbors.

cs.DM↗
arXiv2026

Factorisability of Low Dimensional Non-Negative Integer Matrices

We consider the problem of determining if a given two-dimensional nonnegative integer matrix $M$ is the product of two such matrices, excluding trivial units. A matrix $M$ with no such factorisation is called prime and therefore belongs to the minimal (infinite rank) generator of $2 \times 2$ matrices over the natural numbers, otherwise it is called composite. We also consider the problem of finding a (non-unique) factorisation of a composite matrix. Our results have applications in computational group theory and the theory of codes, where such matrices are called incidence matrices. We analyse the complexity of primality and finding a factorisation for a composite matrix, providing a first efficient algorithm.

cs.DM↗