Related papers: Solving Hypergraph Laplacian Systems in Almost-Lin…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
This paper investigates the behavior of the Min-Sum message passing scheme to solve systems of linear equations in the Laplacian matrices of graphs and to compute electric flows. Voltage and flow problems involve the minimization of…
In this paper we propose a primal-dual homotopy method for $\ell_1$-minimization problems with infinity norm constraints in the context of sparse reconstruction. The natural homotopy parameter is the value of the bound for the constraints…
We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…
We provide an algorithm which, with high probability, maintains a $(1-\epsilon)$-approximate maximum flow on an undirected graph undergoing $m$-edge additions in amortized $m^{o(1)} \epsilon^{-3}$ time per update. To obtain this result, we…
We consider approximation algorithms for the problem of finding $x$ of minimal norm $\|x\|$ satisfying a linear system $\mathbf{A} x = \mathbf{b}$, where the norm $\|\cdot \|$ is arbitrary and generally non-Euclidean. We show a simple…
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…
In this paper we consider graph algorithms in models of computation where the space usage (random accessible storage, in addition to the read only input) is sublinear in the number of edges $m$ and the access to input data is constrained.…
In this paper, we consider the "foreach" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \times N$ matrices $\Phi$ and a decoding algorithm $\algo$ such that for every…
The balanced hypergraph partitioning problem is to partition a hypergraph into $k$ disjoint blocks of bounded size such that the sum of the number of blocks connected by each hyperedge is minimized. We present an improvement to the…
We give the first fully dynamic algorithm which maintains a $(1-\epsilon)$-approximate densest subgraph in worst-case time $\text{poly}(\log n, \epsilon^{-1})$ per update. Dense subgraph discovery is an important primitive for many…
We give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for…
Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the…
We present the first $m\,\text{polylog}(n)$ work, $\text{polylog}(n)$ time algorithm in the PRAM model that computes $(1+\epsilon)$-approximate single-source shortest paths on weighted, undirected graphs. This improves upon the breakthrough…
We develop faster approximation algorithms for Metric-TSP building on recent, nearly linear time approximation schemes for the LP relaxation [Chekuri and Quanrud, 2017]. We show that the LP solution can be sparsified via cut-sparsification…
We formulate and analyze a heterogeneous random hypergraph model, and we provide an achieveability result for recovery of hyperedges from the observed projected graph. We observe a projected graph which combines random hyperedges across all…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…