相关论文: Sparsification of Binary CSPs

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…

High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that…

We derive a new proof to show that the incremental resparsification algorithm proposed by Kelner and Levin (2013) produces a spectral sparsifier in high probability. We rigorously take into account the dependencies across subsequent…

We introduce a technically and conceptually simple approach to magnification of circuit and formula lower bounds. Central to the method are so-called distinguishers, sparse matrices that retain some of the key properties of error-correcting…

This paper presents the first parallel batch-dynamic algorithms for computing spanners and sparsifiers. Our algorithms process any batch of edge insertions and deletions in an $n$-node undirected graph, in $\text{poly}(\log n)$ depth and…

Given a large graph $G$ with a subset $|T|=k$ of its vertices called terminals, a quality-$q$ flow sparsifier is a small graph $G'$ that contains $T$ and preserves all multicommodity flows that can be routed between terminals in $T$, to…

L. A. Bunimovich and B. Z. Webb developed a theory for transforming a finite weighted graph while preserving its spectrum, referred as isospectral reduction theory. In this work we extend this theory to a class of operators on Banach spaces…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

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…

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…

We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…

With fully leveraging the value of unlabeled data, semi-supervised medical image segmentation algorithms significantly reduces the limitation of limited labeled data, achieving a significant improvement in accuracy. However, the…

In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…

Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…

Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss? Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large…

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…

Consider a graph G with an assignment of costs to vertices. Even if G and all its subgraphs admit balanced separators of sublinear size, G may only admit a balanced separator of sublinear cost after deleting a small set Z of exceptional…

We study algorithms for spectral graph sparsification. The input is a graph $G$ with $n$ vertices and $m$ edges, and the output is a sparse graph $\tilde{G}$ that approximates $G$ in an algebraic sense. Concretely, for all vectors $x$ and…

Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…

Let G be an arbitrary finite weighted digraph with weights in the set of complex rational functions. A general procedure is proposed which allows for the reduction of G to a smaller graph with a less complicated structure having the same…