Related papers: Shortest directed networks in the plane
Knowing which nodes are influential in a complex network and whether the network can be influenced by a small subset of nodes is a key part of network analysis. However, many traditional measures of importance focus on node level…
We present randomized algorithms that compute $(1+\epsilon)$-approximate minimum global edge and vertex cuts in weighted directed graphs in $O(\log^4(n) / \epsilon)$ and $O(\log^5(n)/\epsilon)$ single-commodity flows, respectively. With the…
Graphs are called navigable if one can find short paths through them using only local knowledge. It has been shown that for a graph to be navigable, its construction needs to meet strict criteria. Since such graphs nevertheless seem to…
Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…
The widespread relevance of increasingly complex networks requires methods to extract meaningful coarse-grained representations of such systems. For undirected graphs, standard community detection methods use criteria largely based on…
Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…
A Euclidean noncrossing Steiner $(1+\epsilon)$-spanner for a point set $P\subset\mathbb{R}^2$ is a planar straight-line graph that, for any two points $a, b \in P$, contains a path whose length is at most $1+\epsilon$ times the Euclidean…
A sorting network is a shortest path from $12 \cdots n$ to $n \cdots 2 1$ in the Cayley graph of the symmetric group generated by adjacent transpositions. For a uniform random sorting network, we prove that in the global limit, particle…
Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing…
Many physical, biological, and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we offer three…
We consider approximations for computing minimum weighted cuts in directed graphs. We consider both rooted and global minimum cuts, and both edge-cuts and vertex-cuts. For these problems we give randomized Monte Carlo algorithms that…
A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good…
In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
We show that directed minimal cones in (n+1)-dimensional Euclidean space which have at most one singularity are - besides the trivial cases: empty set, whole space - half spaces. Using blow-up techniques, this result can be used to get…
An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error e from 120 degrees.This notion arises in numerical approximations of…
Given a point set $P$ in the Euclidean plane and a parameter $t$, we define an \emph{oriented $t$-spanner} $G$ as an oriented subgraph of the complete bi-directed graph such that for every pair of points, the shortest closed walk in $G$…
Liquid diodes are surface structures that facilitate the flow of liquids in a specific direction. When these structures are within the capillary regime, they promote liquid transport without the need for external forces. In nature, they are…
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…
Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…