相关论文: Exact solutions for the two- and all-terminal reli…
The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations,…
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…
The classic all-terminal network reliability problem posits a graph, each of whose edges fails independently with some given probability.
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
Assume that the vertices of a graph $G$ are always operational, but the edges of $G$ are operational independently with probability $p \in[0,1]$. For fixed vertices $s$ and $t$, the \emph{two-terminal reliability} of $G$ is the probability…
Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem -- to find a network with the best…
Network reliability is an important metric to evaluate the connectivity among given vertices in uncertain graphs. Since the network reliability problem is known as #P-complete, existing studies have used approximation techniques. In this…
The all-terminal reliability of a graph $G$ is the probability that $G$ remains connected when each edge fails independently with probability $p$. For fixed $n$ and $m$, the uniformly most reliable problem asks which graph with $n$ vertices…
The reliability polynomial of a graph gives the probability that a graph remains operational when all its edges could fail independently with a certain fixed probability. In general, the problem of finding uniformly most reliable graphs…
Various real-life applications, for example, Internet of Things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems, are always modeled as network structures.…
In this article, we take a closer look at the reliability of large minimal networks constructed by repeated compositions of the simplest possible networks. For a given number of devices $n=2^m$ we define the set of all the possible…
In the classical s-t network reliability problem a fixed network G is given including two designated vertices s and t (called terminals). The edges are subject to independent random failure, and the task is to compute the probability that s…
Given a graph $G$ in which each edge fails independently with probability $q\in[0,1],$ the all-terminal reliability of $G$ is the probability that all vertices of $G$ can communicate with one another, that is, the probability that the…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
We consider the robust version of a multi-commodity network flow problem. The robustness is defined with respect to the deletion, or failure, of edges. While the flow problem itself is a polynomially-sized linear program, its robust version…