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Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
We consider an Erdos-Renyi random graph consisting of N vertices connected by randomly and independently drawing an edge between every pair of them with probability c/N so that at N->infinity one obtains a graph of finite mean degree c. In…
We define and study two new kinds of "effective resistances" based on hubs-biased -- hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
Stochastic optimization algorithms are widely used for large-scale data analysis due to their low per-iteration costs, but they often suffer from slow asymptotic convergence caused by inherent variance. Variance-reduced techniques have been…
We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…
(First-order) transductions are a basic notion capturing graph modifications that can be described in first-order logic. In this work, we propose an efficient algorithmic method to approximately reverse the application of a transduction,…
Graph Lottery Tickets (GLTs), comprising a sparse adjacency matrix and a sparse graph neural network (GNN), can significantly reduce the inference latency and compute footprint compared to their dense counterparts. Despite these benefits,…
A hypergraph spectral sparsifier of a hypergraph $G$ is a weighted subgraph $H$ that approximates the Laplacian of $G$ to a specified precision. Recent work has shown that similar to ordinary graphs, there exist $\widetilde{O}(n)$-size…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
The problem of learning a directed acyclic graph (DAG) up to Markov equivalence is equivalent to the problem of finding a permutation of the variables that induces the sparsest graph. Without additional assumptions, this task is known to be…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
The mining of frequent subgraphs from labeled graph data has been studied extensively. Furthermore, much attention has recently been paid to frequent pattern mining from graph sequences. A method, called GTRACE, has been proposed to mine…
Resistance distance has been studied extensively in the past years, with the majority of previous studies devoted to undirected networks, in spite of the fact that various realistic networks are directed. Although several generalizations of…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
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…
The problem of inferring unknown graph edges from numerical data at a graph's nodes appears in many forms across machine learning. We study a version of this problem that arises in the field of \emph{landscape genetics}, where genetic…
We introduce a new approach to spectral sparsification that approximates the quadratic form of the pseudoinverse of a graph Laplacian restricted to a subspace. We show that sparsifiers with a near-linear number of edges in the dimension of…
Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such…