Related papers: Vertex Sparsification for Edge Connectivity
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
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…
A cut sparsifier is a reweighted subgraph that maintains the weights of the cuts of the original graph up to a multiplicative factor of $(1\pm\epsilon)$. This paper considers computing cut sparsifiers of weighted graphs of size $O(n\log…
In vertex-cut sparsification, given a graph $G=(V,E)$ with a terminal set $T\subseteq V$, we wish to construct a graph $G'=(V',E')$ with $T\subseteq V'$, such that for every two sets of terminals $A,B\subseteq T$, the size of a minimum…
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 current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…
We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-$k$-ECSS problem, we are given a graph $G=(V,E)$ whose edges have non-negative…
In this paper, we study a \emph{multicut-mimicking network} for a hypergraph over terminals $T$ with a parameter $c$. It is a hypergraph preserving the minimum multicut values of any set of pairs over $T$ where the value is at most $c$.…
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…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
In the load-balancing problem, we have an $n$-vertex bipartite graph $G=(L, R, E)$ between a set of clients and servers. The goal is to find an assignment of all clients to the servers, while minimizing the maximum load on each server,…
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…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
Network epidemiology has become a vital tool in understanding the effects of high-degree vertices, geographic and demographic communities, and other inhomogeneities in social structure on the spread of disease. However, many networks…
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,…
The message-passing paradigm of Graph Neural Networks often struggles with exchanging information across distant nodes typically due to structural bottlenecks in certain graph regions, a limitation known as \textit{over-squashing}. To…
Let $G$ be a graph and $S, T \subseteq V(G)$ be (possibly overlapping) sets of terminals, $|S|=|T|=k$. We are interested in computing a vertex sparsifier for terminal cuts in $G$, i.e., a graph $H$ on a smallest possible number of vertices,…
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…
How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…
Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient…