Related papers: Online Algorithms for Spectral Hypergraph Sparsifi…
This work presents inGRASS, a novel algorithm designed for incremental spectral sparsification of large undirected graphs. The proposed inGRASS algorithm is highly scalable and parallel-friendly, having a nearly-linear time complexity for…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…
To cope with the complexity of large networks, a number of dimensionality reduction techniques for graphs have been developed. However, the extent to which information is lost or preserved when these techniques are employed has not yet been…
Spectral sparsification for directed Eulerian graphs is a key component in the design of fast algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system solvers are crucial algorithmic primitives to fast…
Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three…
We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular…
Spectral graph sparsification aims to find ultra-sparse subgraphs which can preserve spectral properties of original graphs. In this paper, a new spectral criticality metric based on trace reduction is first introduced for identifying…
We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications,…
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…
We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates…
We study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on…
For edge coloring, the online and the W-streaming models seem somewhat orthogonal: the former needs edges to be assigned colors immediately after insertion, typically without any space restrictions, while the latter limits memory to…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
Network embedding aims to learn low-dimensional representations of nodes in a network, while the network structure and inherent properties are preserved. It has attracted tremendous attention recently due to significant progress in…