Related papers: Local Algorithms for Bounded Degree Sparsifiers in…
We initiate a systematic study of algorithms that are both differentially private and run in sublinear time for several problems in which the goal is to estimate natural graph parameters. Our main result is a differentially-private…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…
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…
The intersection graph induced by a set $\Disks$ of $n$ disks can be dense. It is thus natural to try and sparsify it, while preserving connectivity. Unfortunately, sparse graphs can always be made disconnected by removing a small number of…
Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models. We present improved streaming algorithms for approximating…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required. We propose a method of network…
CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…
We study the problem of compressing a weighted graph $G$ on $n$ vertices, building a "sketch" $H$ of $G$, so that given any vector $x \in \mathbb{R}^n$, the value $x^T L_G x$ can be approximated up to a multiplicative $1+\epsilon$ factor…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…
Recently, Chalermsook et al. [SODA'21(arXiv:2007.07862)] introduces a notion of vertex sparsifiers for $c$-edge connectivity, which has found applications in parameterized algorithms for network design and also led to exciting dynamic…
Given a graph $G$ of degree $k$ over $n$ vertices, we consider the problem of computing a near maximum cut or a near minimum bisection in polynomial time. For graphs of girth $2L$, we develop a local message passing algorithm whose…
For any undirected and weighted graph $G=(V,E,w)$ with $n$ vertices and $m$ edges, we call a sparse subgraph $H$ of $G$, with proper reweighting of the edges, a $(1+\varepsilon)$-spectral sparsifier if \[…
Maximum matching is one of the most fundamental combinatorial optimization problems with applications in various contexts such as balanced clustering, data mining, resource allocation, and online advertisement. In many of these…
The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…
Given an undirected graph $G$ and an error parameter $\epsilon > 0$, the {\em graph sparsification} problem requires sampling edges in $G$ and giving the sampled edges appropriate weights to obtain a sparse graph $G_{\epsilon}$ with the…
Graph Neural Networks (GNNs) have demonstrated superior performance across various graph learning tasks but face significant computational challenges when applied to large-scale graphs. One effective approach to mitigate these challenges is…
In this paper, we present a construction of a `matching sparsifier', that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to…