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Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…
A general information transmission model, under independent and identically distributed Gaussian codebook and nearest neighbor decoding rule with processed channel output, is investigated using the performance metric of generalized mutual…
The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…
Consider binary linear codes obtained from bipartite graphs as follows. There are~\(k \geq 1\) left nodes each representing a message bit and there are~\(m = m(k)\) right nodes each representing a parity bit, generated from the…
In this paper, we study the problem of graph compression with side information at the decoder. The focus is on the situation when an unlabelled graph (which is also referred to as a structure) is to be compressed or is available as side…
We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired…
The transmission of digital data is one of the principal tasks in modern wireless communication. Classically, the communication channel consists of one transmitter and one receiver; however, due to the constantly increasing demand in higher…
We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…
Graph neural networks can be effectively applied to find solutions for many real-world problems across widely diverse fields. The success of graph neural networks is linked to the message-passing mechanism on the graph, however, the…
In this paper we consider the fundamental problem of approximating the diameter $D$ of directed or undirected graphs. In a seminal paper, Aingworth, Chekuri, Indyk and Motwani [SIAM J. Comput. 1999] presented an algorithm that computes in…
We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
The problem of recovering graph signals is one of the main topics in graph signal processing. A representative approach to this problem is the graph Wiener filter, which utilizes the statistical information of the target signal computed…
We consider statistical graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. This general model encompasses various signals such as the traditional…
We derive standard imsets for undirected graphical models and chain graphical models. Standard imsets for undirected graphical models are described in terms of minimal triangulations for maximal prime subgraphs of the undirected graphs. For…
In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity.…
The subject of this paper is transmission over a general class of binary-input memoryless symmetric channels using error correcting codes based on sparse graphs, namely low-density generator-matrix and low-density parity-check codes. The…
We introduce the concept of shallow directed minors and based on this a new classification of classes of directed graphs which is diametric to existing directed graph decompositions and width measures proposed in the literature. We then…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
We study property testing of (di)graph properties in bounded-degree graph models. The study of graph properties in bounded-degree models is one of the focal directions of research in property testing in the last 15 years. However, despite…
This paper considers the transmission of an infinite sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. While…