Related papers: Exact two-terminal reliability of some directed ne…
The availability of data from many different sources and fields of science has made it possible to map out an increasing number of networks of contacts and interactions. However, quantifying how reliable these data are remains an open…
A two-terminal graph is a graph G equipped with two vertices in V(G) called terminals. Let T(n,m) be the set of two-terminal graphs on n vertices and m edges. Let G be in T(n,m) and let p be in [0,1]. The two-terminal reliability of G at p,…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
We give a fully polynomial-time randomized approximation scheme (FPRAS) for the all-terminal network reliability problem, which is to determine the probability that, in a undirected graph, assuming each edge fails independently, the…
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…
A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability $p$. One can ask for the probability that all vertices can communicate ({\em all-terminal…
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…
We study the robustness of interdependent networks where two networks are said to be interdependent if the operation of one network depends on the operation of the other one, and vice versa. In this paper, we propose a model for analyzing…
The routing algorithms for parallel computers, on-chip networks, multi-core processors, and multiprocessors system-on-chip (MP-SoCs) exhibit router failures must be able to handle interconnect router failures that render a symmetrical mesh…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional…
Uncertain, or probabilistic, graphs have been increasingly used to represent noisy linked data in many emerging applications, and have recently attracted the attention of the database research community. A fundamental problem on uncertain…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
The resilience of a complex interconnected system concerns the size of the macroscopic functioning node clusters after external perturbations based on a random or designed scheme. For a representation of the interconnected systems with…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
To achieve fast recovery from link failures, most modern communication networks feature fully decentralized fast re-routing mechanisms. These re-routing mechanisms rely on pre-installed static re-routing rules at the nodes (the routers),…
In this paper, we consider reachability oracles and reachability preservers for directed graphs/networks prone to edge/node failures. Let $G = (V, E)$ be a directed graph on $n$-nodes, and $P\subseteq V\times V$ be a set of vertex pairs in…
To capture the systemic complexity of international financial systems, network data is an important prerequisite. However, dyadic data is often not available, raising the need for methods that allow for reconstructing networks based on…
An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…