Related papers: Compressing bipartite graphs with a dual reorderin…
The bipartite graph structure has shown its promising ability in facilitating the subspace clustering and spectral clustering algorithms for large-scale datasets. To avoid the post-processing via k-means during the bipartite graph…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…
As large-scale graphs become increasingly more prevalent, it poses significant computational challenges to process, extract and analyze large graph data. Graph coarsening is one popular technique to reduce the size of a graph while…
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while…
In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
Training Graph Neural Networks (GNNs) on large graphs presents unique challenges due to the large memory and computing requirements. Distributed GNN training, where the graph is partitioned across multiple machines, is a common approach to…
Given a sufficiently large and sufficiently dense bipartite graph $G=(A, B; E),$ we present a novel method for decomposing the majority of the edges of $G$ into quasirandom graphs so that the vertex sets of these quasirandom graphs…
Model compression has gained significant popularity as a means to alleviate the computational and memory demands of machine learning models. Each compression technique leverages unique features to reduce the size of neural networks.…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
Real-world graphs are massive in size and we need a huge amount of space to store them. Graph compression allows us to compress a graph so that we need a lesser number of bits per link to store it. Of many techniques to compress a graph, a…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…
Compression of inverted lists with methods that support fast intersection operations is an active research topic. Most compression schemes rely on encoding differences between consecutive positions with techniques that favor small numbers.…
In this work, we establish theoretical and practical connections between vertex indexing for sparse graph/network compression and matrix ordering for sparse matrix-vector multiplication and variable elimination. We present a fundamental…
Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work,…
Large-scale datasets in the form of knowledge graphs are often used in numerous domains, today. A knowledge graphs size often exceeds the capacity of a single computer system, especially if the graph must be stored in main memory. To…
We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph partitionings. The adaptivity of the partitionings, a key…
Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from…
This paper proposes an efficient method to construct the bipartite graph with as many edges as possible while without introducing the shortest cycles of length equal to 4. The binary matrix associated with the bipartite graph described…