Related papers: Engineering an algorithm for constructing low-stre…

Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…

We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent…

The attention mechanism has demonstrated superior performance for inference over nodes in graph neural networks (GNNs), however, they result in a high computational burden during both training and inference. We propose FastGAT, a method to…

Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse…

Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…

We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection. It is based on nested dissection, sparsification and low-rank compression. After…

We address the problem of computing the distribution of induced connected subgraphs, aka \emph{graphlets} or \emph{motifs}, in large graphs. The current state-of-the-art algorithms estimate the motif counts via uniform sampling, by…

Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…

Recent advances in graph processing on FPGAs promise to alleviate performance bottlenecks with irregular memory access patterns. Such bottlenecks challenge performance for a growing number of important application areas like machine…

Let $P \subset \mathbb{R}^2$ be a planar $n$-point set such that each point $p \in P$ has an associated radius $r_p > 0$. The transmission graph $G$ for $P$ is the directed graph with vertex set $P$ such that for any $p, q \in P$, there is…

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…

Graph-based nearest neighbor search methods have seen a surge of popularity in recent years, offering state-of-the-art performance across a wide variety of applications. Central to these methods is the task of constructing a sparse…

Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream…

We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…

Given a connected graph $G=(V,E)$ and a length function $\ell:E\to {\mathbb R}$ we let $d_{v,w}$ denote the shortest distance between vertex $v$ and vertex $w$. A $t$-spanner is a subset $E'\subseteq E$ such that if $d'_{v,w}$ denotes…

In this paper we consider the problem of efficiently constructing $k$-vertex fault-tolerant geometric $t$-spanners in $\dspace$ (for $k \ge 0$ and $t >1$). Vertex fault-tolerant spanners were introduced by Levcopoulus et. al in 1998. For…

Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…

Shortest path computation is one of the most fundamental operations for managing and analyzing large social networks. Though existing techniques are quite effective for finding the shortest path on large but sparse road networks, social…

Discrepancy theory provides powerful tools for producing higher-quality objects which "beat the union bound" in fundamental settings throughout combinatorics and computer science. However, this quality has often come at the price of more…

We propose a novel algorithm for enumerating and listing all minimal cutsets of a given graph. It is known that this problem is NP-hard. We use connectivity properties of a given graph to develop an algorithm with reduced complexity for…