Related papers: Fully Dynamic Spectral Sparsification of Hypergrap…
Graph Neural Networks (GNNs) are widely used to perform different machine learning tasks on graphs. As the size of the graphs grows, and the GNNs get deeper, training and inference time become costly in addition to the memory requirement.…
Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…
We present several sparsification lower and upper bounds for classic problems in graph theory and logic. For the problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is no polynomial-time…
We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph $G$ on $n$ vertices described by a binary string of length $N$, an integer $k\leq \log n$,…
Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks…
Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and insertions. It is one of the most…
We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear…
Network sparsification is the task of reducing the number of edges of a given graph while preserving some crucial graph property. In community-aware network sparsification, the preserved property concerns the subgraphs that are induced by…
A motif is a frequently occurring subgraph of a given directed or undirected graph $G$. Motifs capture higher order organizational structure of $G$ beyond edge relationships, and, therefore, have found wide applications such as in graph…
Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…
We introduce a notion of code sparsification that generalizes the notion of cut sparsification in graphs. For a (linear) code $\mathcal{C} \subseteq \mathbb{F}_q^n$ of dimension $k$ a $(1 \pm \epsilon)$-sparsification of size $s$ is given…
Let $H=(V,E)$ be an edge-weighted hypergraph of rank $r$. Kogan and Krauthgamer extended Bencz\'{u}r and Karger's random sampling scheme for cut sparsification from graphs to hypergraphs. The sampling requires an algorithm for computing the…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
We study maximum matchings in fully dynamic graphs, which are graphs that undergo both edge insertions and deletions. Our focus is on algorithms that estimate the size of maximum matching after each update while spending a small time. An…
As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However,…
The Kadison-Singer Conjecture, as proved by Marcus, Spielman, and Srivastava (MSS) [Ann. Math. 182, 327-350 (2015)], has been informally thought of as a strengthening of Batson, Spielman, and Srivastava's theorem that every undirected graph…
Recently there has been much interest in "sparsifying" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that results from the sum. Results of this sort have…
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…
In this paper we consider the \emph{fully-dynamic} All-Pairs Effective Resistance problem, where the goal is to maintain effective resistances on a graph $G$ among any pair of query vertices under an intermixed sequence of edge insertions…
The use of tools from analysis to approach problems in graph theory has become an active area of research. Usually such methods are applied to problems involving dense graphs and hypergraphs; here we give the an extension of such methods to…