Related papers: Graph Sparsification in the Semi-streaming Model
Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely…
In graph sparsification, the goal has almost always been of {global} nature: compress a graph into a smaller subgraph ({sparsifier}) that maintains certain features of the original graph. Algorithms can then run on the sparsifier, which in…
In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy…
Traditional graph-based semi-supervised learning (SSL) approaches, even though widely applied, are not suited for massive data and large label scenarios since they scale linearly with the number of edges $|E|$ and distinct labels $m$. To…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which…
Flow sparsification is a classic graph compression technique which, given a capacitated graph $G$ on $k$ terminals, aims to construct another capacitated graph $H$, called a flow sparsifier, that preserves, either exactly or approximately,…
Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…
While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a…
As graphs scale to billions of nodes and edges, graph Machine Learning workloads are constrained by the cost of multi-hop traversals over exponentially growing neighborhoods. While various system-level and algorithmic optimizations have…
In this paper we give a construction of cut sparsifiers of Benczur and Karger in the {\em dynamic} streaming setting in a single pass over the data stream. Previous constructions either required multiple passes or were unable to handle edge…
A sparsifier of a graph $G$ (Bencz\'ur and Karger; Spielman and Teng) is a sparse weighted subgraph $\tilde G$ that approximately retains the cut structure of $G$. For general graphs, non-trivial sparsification is possible only by using…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…
In this paper, we study the problem of finding a maximum matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, an algorithm receives a stream of edges and it is allowed to have a memory of…
Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater…
Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear…
We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory…