Related papers: Communication Costs in a Geometric Communication N…
This paper surveys visualization and interaction techniques for geospatial networks from a total of 95 papers. Geospatial networks are graphs where nodes and links can be associated with geographic locations. Examples can include social…
We explore the connection between dimensionality and communication cost in distributed learning problems. Specifically we study the problem of estimating the mean $\vec{\theta}$ of an unknown $d$ dimensional gaussian distribution in the…
We consider a number of fundamental statistical and graph problems in the message-passing model, where we have $k$ machines (sites), each holding a piece of data, and the machines want to jointly solve a problem defined on the union of the…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
The general communication tree embedding problem is the problem of mapping a set of communicating terminals, represented by a graph G, into the set of vertices of some physical network represented by a tree T. In the case where the vertices…
Let $G$ be a connected graph on $n$ vertices and $C$ be an $(n,k,d)$ code with $d\ge 2$, defined on the alphabet set $\{0,1\}^m$. Suppose that for $1\le i\le n$, the $i$-th vertex of $G$ holds an input symbol $x_i\in\{0,1\}^m$ and let…
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…
We consider a Min-Power Bounded-Hops Symmetric Connectivity problem that consists in the construction of communication spanning tree on a given graph, where the total energy consumption spent for the data transmission is minimized and the…
Communication of signals among nodes in a complex network poses fundamental problems of efficiency and cost. Routing of messages along shortest paths requires global information about the topology, while spreading by diffusion, which…
Consider the classical problem of information dissemination: one (or more) nodes in a network have some information that they want to distribute to the remainder of the network. In this paper, we study the cost of information dissemination…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
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…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
Motivated by the increasing interest in applications of graph geodesic convexity in machine learning and data mining, we present a heuristic for computing the geodesic convex hull of node sets in networks. It generates a set of almost…
The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an…
A process of preparation, transmission and subsequent projective measurement of a qubit can be simulated by a classical model with only two bits of communication and some amount of shared randomness. However no model for n qubits with a…
Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would…
We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are…