Splitting the K-Terminal Reliability

TL;DR

This paper introduces an efficient splitting formula for calculating the K-terminal reliability in a graph, utilizing lattice theoretic methods to improve computational efficiency when a separating vertex set exists.

Contribution

The paper presents a novel splitting formula for K-terminal reliability based on lattice theory, enhancing computational methods for reliability analysis in graphs.

Findings

Provides an efficient splitting formula for K-terminal reliability

Utilizes lattice theoretic methods for reliability computation

Applicable to graphs with separating vertex sets

Abstract

Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article we propose an efficient splitting formula for R(G,K) at a separating vertex set of G by lattice theoretic methods.