Related papers: Greedy Connectivity of Geographically Embedded Gra…
An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map on homology from a…
In greedy geometric routing, messages are passed in a network embedded in a metric space according to the greedy strategy of always forwarding messages to nodes that are closer to the destination. We show that greedy geometric routing…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a…
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…
In this paper we consider the problem of optimizing the ecological connectivity of a landscape under a budget constraint by improving habitat areas and ecological corridors between them. We consider a formulation of this problem in terms of…
We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Directed graphs provide more subtle and precise modelling tools for optimization in road networks than simple graphs. In particular, they are more suitable in the context of alternative fuel vehicles and new automotive technologies, like…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of…
For the classical maximum coverage problem, the greedy algorithm achieves a worst-case $1-1/e$ approximation, which is optimal unless $\text{P} = \text{NP}$. The notion of coverage appears in a wide range of optimization tasks, where…
Today's networks consist of many autonomous entities that follow their own objectives, i.e., smart devices or parts of large AI systems, that are interconnected. Given the size and complexity of most communication networks, each entity…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…
Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $R^n$, with the admissible set indexed by the time parameter. The…
The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent…
Given a graph $G=(V,E)$, suppose we are interested in selecting a sequence of vertices $(x_j)_{j=1}^n$ such that $\left\{x_1, \dots, x_k\right\}$ is `well-distributed' uniformly in $k$. We describe a greedy algorithm motivated by potential…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
Navigability of networks, that is the ability to find any given destination vertex starting from any other vertex, is crucial to their usefulness. In 2000 Kleinberg showed that optimal navigability could be achieved in small-world networks…
Graph-based approaches are empirically shown to be very successful for the nearest neighbor search (NNS). However, there has been very little research on their theoretical guarantees. We fill this gap and rigorously analyze the performance…