Related papers: Engineering Data Reduction for Nested Dissection
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
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…
Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
For distributed graph processing on massive graphs, a graph is partitioned into multiple equally-sized parts which are distributed among machines in a compute cluster. In the last decade, many partitioning algorithms have been developed…
In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…
We present Roadmap Sparsification by Edge Contraction (RSEC), a simple and effective algorithm for reducing the size of a motion-planning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…
Efficiently solving sparse linear systems $Ax=b$, where $A$ is a large, sparse, symmetric positive semi-definite matrix, is a core challenge in scientific computing, machine learning, and optimization. A major bottleneck in Gaussian…
Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…
We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…
We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem is based on interior point methods (IPMs) and…