Related papers: Fast C-K-R Partitions of Sparse Graphs

Many applications require randomly sampling bipartite graphs with fixed degrees, or randomly sampling incidence matrices with fixed row and column sums. Although several sampling algorithms exist, the ``curveball'' algorithm is the most…

In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…

We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…

The Marcus-Spielman-Srivastava theorem (Annals of Mathematics, 2015) for the Kadison-Singer conjecture implies the following result in spectral graph theory: For any undirected graph $G = (V,E)$ with a maximum edge effective resistance at…

We consider the problem of partitioning the edges of a graph into as few paths as possible. This is a~subject of the classic conjecture of Gallai and a recurring topic in combinatorics. Regarding the complexity of partitioning a graph…

We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…

In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \rightarrow \mathbb{R}$ with a…

Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present SURF, an algorithm for approximating distributions by piecewise polynomials. SURF is: simple, replacing…

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…

Graphs are useful to interpret widely used image processing methods, e.g., bilateral filtering, or to develop new ones, e.g., kernel based techniques. However, simple graph constructions are often used, where edge weight and connectivity…

We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition.…

Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…

We present a simple mechanism, which can be randomised, for constructing sparse $3$-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over $\mathbb{Z}_2^t$ and have vertex degree…

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

This paper gives new, efficient algorithms for approximate uniform sampling of contingency tables and integer partitions. The algorithms use the Burnside process, a general algorithm for sampling a uniform orbit of a finite group acting on…

Simply put, a sparse polynomial is one whose zero coefficients are not explicitly stored. Such objects are ubiquitous in exact computing, and so naturally we would like to have efficient algorithms to handle them. However, with this compact…

Let $G=(V, E)$ be an undirected $n$-vertices $m$-edges graph with non-negative edge weights. In this paper, we present three new algorithms for constructing a $(2k-1)$-stretch distance oracle with $O(n^{1+\frac{1}{k}})$ space. The first…

We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…