Related papers: A New Approach to Laplacian Solvers and Flow Probl…
We establish the convergence of the min-sum message passing algorithm for minimization of a broad class of quadratic objective functions: those that admit a convex decomposition. Our results also apply to the equivalent problem of the…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1-\epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem.…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
We present a novel quantum walk-based approach to solve the Minimum Spanning Tree (MST) problem under a maximal degree constraint (MDC). By recasting the classical MST problem as a quantum walk on a graph, where vertices are encoded as…
We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…
This paper considers and proposes some algorithms to compute the mean curvature flow under topological changes. Instead of solving the fully nonlinear partial differential equations based on the level set approach, we propose some…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
We study minimum vertex cover problems on random \alpha-uniform hypergraphs using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm. It is found that there exists a phase…
We present an $m^{4/3+o(1)}\log W$-time algorithm for solving the minimum cost flow problem in graphs with unit capacity, where $W$ is the maximum absolute value of any edge weight. For sparse graphs, this improves over the best known…
We consider decentralized optimization problems in which a number of agents collaborate to minimize the average of their local functions by exchanging over an underlying communication graph. Specifically, we place ourselves in an…
This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…