Related papers: A Parallel Solver for Graph Laplacians
The ability to timely process significant amounts of continuously updated spatial data is mandatory for an increasing number of applications. Parallelism enables such applications to face this data-intensive challenge and allows the devised…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
Counting k-cliques in a graph is an important problem in graph analysis with many applications such as community detection and graph partitioning. Counting k-cliques is typically done by traversing search trees starting at each vertex in…
This paper develops an algebraic multigrid preconditioner for the graph Laplacian. The proposed approach uses aggressive coarsening based on the aggregation framework in the setup phase and a polynomial smoother with sufficiently large…
Graph processing at scale presents many challenges, including the irregular structure of graphs, the latency-bound nature of graph algorithms, and the overhead associated with distributed execution. While existing frameworks such as Spark…
The One Sided Crossing Minimization (OSCM) problem is an optimization problem in graph drawing that aims to minimize the number of edge crossings in bipartite graph layouts. It has practical applications in areas such as network…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
While Graph Neural Networks (GNNs) are popular in the deep learning community, they suffer from several challenges including over-smoothing, over-squashing, and gradient vanishing. Recently, a series of models have attempted to relieve…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
Sparse graphs are ubiquitous in real and virtual worlds. With the phenomenal growth in semi-structured and unstructured data, sizes of the underlying graphs have witnessed a rapid growth over the years. Analyzing such large structures…
In this work we study statistical properties of graph-based algorithms for multi-manifold clustering (MMC). In MMC the goal is to retrieve the multi-manifold structure underlying a given Euclidean data set when this one is assumed to be…
To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…
Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…
How might one "reduce" a graph? That is, generate a smaller graph that preserves the global structure at the expense of discarding local details? There has been extensive work on both graph sparsification (removing edges) and graph…
Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering…