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We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
Viability of electric vehicle car sharing operations depends on rebalancing algorithms. Earlier methods in the literature suggest a trend toward Markovian stochastic demand with server relocation with queueing constraints. We propose a new…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…
Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the…
We investigate random processes for generating task-dependency graphs of order $n$ with $m$ edges and a specified number of initial vertices and terminal vertices. In order to do so, we consider two random processes for generating…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms…
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks…
Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at the assumptions they make on the underlying network. We investigate this question from the perspective of network…
The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…
Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
We consider the following load balancing process for $m$ tokens distributed arbitrarily among $n$ nodes connected by a complete graph: In each time step a pair of nodes is selected uniformly at random. Let $\ell_1$ and $\ell_2$ be their…
Graph-based learning is a rapidly growing sub-field of machine learning with applications in social networks, citation networks, and bioinformatics. One of the most popular models is graph attention networks. They were introduced to allow a…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
Let $G$ be an undirected graph. An edge of $G$ dominates itself and all edges adjacent to it. A subset $E'$ of edges of $G$ is an edge dominating set of $G$, if every edge of the graph is dominated by some edge of $E'$. We say that $E'$ is…
In this article we introduce a dynamic Erd\H{o}s-R\'enyi graph model, in which, independently for each vertex pair, edges appear and disappear according to a Markov on-off process. In studying the dynamic graph we present two main results.…