Related papers: Every Schnyder Drawing is a Greedy Embedding
The algorithmic small-world phenomenon, empirically established by Milgram's letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from today's perspective his model has several severe…
Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph…
Telemetry-Aware routing promises to increase efficacy and responsiveness to traffic surges in computer networks. Recent research leverages Machine Learning to deal with the complex dependency between network state and routing, but…
Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods…
We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…
We study {\sc greedy} routing over $n$ nodes placed in a ring, with the \emph{distance} between two nodes defined to be the clockwise or the absolute distance between them along the ring. Such graphs arise in the context of modeling social…
Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph…
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…
In the 1960s, the social scientist Stanley Milgram performed his famous "small-world" experiments where he found that people in the US who are far apart geographically are nevertheless connected by remarkably short chains of acquaintances.…
We present a local routing algorithm which guarantees delivery in all connected graphs embedded on a known surface of genus $g$. The algorithm transports $O(g\log n)$ memory and finishes in time $O(g^2n^2)$, where $n$ is the size of the…
The graph layouts used for complex network studies have been mainly been developed to improve visualization. If we interpret the layouts in metric spaces such as Euclidean ones, however, the embedded spatial information can be a valuable…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
A geometric graph is a graph embedded in the plane with vertices at points and edges drawn as curves (which are usually straight line segments) between those points. The average transversal complexity of a geometric graph is the number of…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…
Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require…
Geographic routing consists in using the position information of nodes to assist in the routing process, and has been a widely studied subject in sensor networks. One of the outstanding challenges facing geographic routing has been its…
In this paper, we design a greedy routing on networks of mobile agents. In the greedy routing algorithm, every time step a packet in agent $i$ is delivered to the agent $j$ whose distance from the destination is shortest among searched…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
An ordering of the vertices of a graph is \emph{connected} if every vertex (but the first) has a neighbor among its predecessors. The greedy colouring algorithm of a graph with a connected order consists in taking the vertices in order, and…