Related papers: The Sketching Complexity of Graph and Hypergraph C…

Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is $k$-connected if it remains connected after removing any $k-1$ vertices. The vertex connectivity of a graph is the maximum $k$ such that…

While message passing Graph Neural Networks (GNNs) have become increasingly popular architectures for learning with graphs, recent works have revealed important shortcomings in their expressive power. In response, several higher-order GNNs…

Consider the following gap cycle counting problem in the streaming model: The edges of a $2$-regular $n$-vertex graph $G$ are arriving one-by-one in a stream and we are promised that $G$ is a disjoint union of either $k$-cycles or…

Higher-order interactions beyond pairwise relationships in large complex networks are often modeled as hypergraphs. Analyzing hypergraph properties such as triad counts is essential, as hypergraphs can reveal intricate group interaction…

Modern stream processing systems often need to track the frequency of distinct keys in a data stream in real-time. Since maintaining exact counts can require a prohibitive amount of memory, many applications rely on compact, probabilistic…

Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…

The blooming availability of traces for social, biological, and communication networks opens up unprecedented opportunities in analyzing diffusion processes in networks. However, the sheer sizes of the nowadays networks raise serious…

Computing cohesive subgraphs is a central problem in graph theory. While many formulations of cohesive subgraphs lead to NP-hard problems, finding a densest subgraph can be done in polynomial time. As such, the densest subgraph model has…

Graph learning algorithms have attained state-of-the-art performance on many graph analysis tasks such as node classification, link prediction, and clustering. It has, however, become hard to track the field's burgeoning progress. One…

The seminal work of Ahn, Guha, and McGregor in 2012 introduced the graph sketching technique and used it to present the first streaming algorithms for various graph problems over dynamic streams with both insertions and deletions of edges.…

We consider an approach for community detection in time-varying networks. At its core, this approach maintains a small sketch graph to capture the essential community structure found in each snapshot of the full network. We demonstrate how…

Graph processing has become an important part of various areas of computing, including machine learning, medical applications, social network analysis, computational sciences, and others. A growing amount of the associated graph processing…

In this paper, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph $H$, but on the frequency with which a vertex or an edge belongs to such…

The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This…

The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…

Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…

We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…

Finding the connected components of a graph is a fundamental problem with uses throughout computer science and engineering. The task of computing connected components becomes more difficult when graphs are very large, or when they are…

Subgraphs such as cliques, loops and stars form crucial connections in the topologies of real-world networks. Random graph models provide estimates for how often certain subgraphs appear, which in turn can be tested against real-world…