Related papers: On lossy Compression of Directed Graphs
In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…
As graph-structured data grow increasingly large, evaluating their robustness under adversarial attacks becomes computationally expensive and difficult to scale. To address this challenge, we propose to compress graphs into compact…
A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
Graph pattern matching, one of the fundamental graph mining problems, aims to extract structural patterns of interest from an input graph. The state-of-the-art graph matching algorithms and systems are mainly designed for undirected graphs.…
With the increasing demands of training graph neural networks (GNNs) on large-scale graphs, graph data condensation has emerged as a critical technique to relieve the storage and time costs during the training phase. It aims to condense the…
In a series of three papers we develop an end space theory for directed graphs. As for undirected graphs, the ends of a digraph are points at infinity to which its rays converge. Unlike for undirected graphs, some ends are joined by limit…
To deal with irregular data structure, graph convolution neural networks have been developed by a lot of data scientists. However, data scientists just have concentrated primarily on developing deep neural network method for un-directed…
We study the rate-distortion problem for both scalar and vector memoryless heavy-tailed $\alpha$-stable sources ($0 < \alpha < 2$). Using a recently defined notion of ``strength" as a power measure, we derive the rate-distortion function…
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking whether this relationship lifts to directed graphs -- we…
Today's networks are controlled assuming pre-compressed and packetized data. For video, this assumption of data packets abstracts out one of the key aspects - the lossy compression problem. Therefore, first, this paper develops a framework…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
A DAG compression of a (typically dense) graph is a simple data structure that stores how vertex clusters are connected, where the clusters are described indirectly as sets of reachable sinks in a directed acyclic graph (DAG). They…
This paper presents a one shot analysis of the lossy compression problem under average distortion constraints. We calculate the exact expected distortion of a random code. The result is given as an integral formula using a newly defined…
In this paper we give a short theoretical description of the general predictive adaptive arithmetic coding technique. The links between this technique and the works of J. Rissanen in the 80's, in particular the BIC information criterion…
We describe a rational approach to reduce the computational and communication complexities of lossless point-to-point compression for computation with side information. The traditional method relies on building a characteristic graph with…
The primary goal of this work is to review the importance of data compression and present a fast Fourier-based method for generating the deterministic compression matrix in the area of deterministic compressed sensing. The principle…
In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for…