Related papers: Quantum Speedup for Graph Sparsification, Cut Appr…
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…
In this paper we introduce a notion of spectral approximation for directed graphs. While there are many potential ways one might define approximation for directed graphs, most of them are too strong to allow sparse approximations in…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
Graph sparsification is an area of interest in computer science and applied mathematics. Sparsification of a graph, in general, aims to reduce the number of edges in the network while preserving specific properties of the graph, like cuts…
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…
A $(1 \pm \epsilon)$-sparsifier of a hypergraph $G(V,E)$ is a (weighted) subgraph that preserves the value of every cut to within a $(1 \pm \epsilon)$-factor. It is known that every hypergraph with $n$ vertices admits a $(1 \pm…
Given a weighted 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 $G_{\epsilon}$ (containing…
Graph sketching has emerged as a powerful technique for processing massive graphs that change over time (i.e., are presented as a dynamic stream of edge updates) over the past few years, starting with the work of Ahn, Guha and McGregor…
We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs $G$ and $W$ and an integer $k$, we are asked to find a $k$-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…
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…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple…
We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same…
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…
This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We…
We provide an algorithm that, given an $n$-vertex $m$-edge Eulerian graph with polynomially bounded weights, computes an $\breve{O}(n\log^{2} n \cdot \varepsilon^{-2})$-edge $\varepsilon$-approximate Eulerian sparsifier with high…
We introduce a novel hybrid quantum-analog algorithm to perform graph clustering that exploits connections between the evolution of dynamical systems on graphs and the underlying graph spectra. This approach constitutes a new class of…