Related papers: Optimal algebraic Breadth-First Search for sparse …
The increase in the dimensionality of neural embedding models has enhanced the accuracy of semantic search capabilities but also amplified the computational demands for Approximate Nearest Neighbor Searches (ANNS). This complexity poses…
We present a new fast all-pairs shortest path algorithm for unweighted graphs. In breadth-first search which is said to representative and fast in unweighted graphs, the average number of accesses to adjacent vertices (expressed by…
The purpose of this report is to explain how the textbook breadth-first search algorithm (BFS) can be modified in order to also create a compact representation of all shortest paths connecting a single source node to all the nodes reachable…
Deep Neural Networks are powerful tools for solving machine learning problems, but their training often involves dense and costly parameter updates. In this work, we use a novel Max-Plus neural architecture in which classical addition and…
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…
Graph Spectral Sparsification (GSS) identifies an ultra-sparse subgraph, or sparsifier, whose Laplacian matrix closely approximates the spectral properties of the original graph, enabling substantial reductions in computational complexity…
The GraphBLAS high performance library standard has yielded capabilities beyond enabling graph algorithms to be readily expressed in the language of linear algebra. These GraphBLAS capabilities enable new performant ways of thinking about…
BFS (Breadth-First Search) is a typical graph algorithm used as a key component of many graph applications. However, current distributed parallel BFS implementations suffer from irregular data communication with large volumes of transfers…
Depth-first search (DFS) is the basis for many efficient graph algorithms. We introduce general techniques for the efficient implementation of DFS-based graph algorithms and exemplify them on three algorithms for computing strongly…
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…
Graph algorithms enormously contribute to the domains such as blockchains, social networks, biological networks, telecommunication networks, and several others. The ever-increasing demand of data-volume, as well as speed of such…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…
We present the first parallel depth-first search algorithm for undirected graphs that has near-linear work and sublinear depth. Concretely, in any $n$-node $m$-edge undirected graph, our algorithm computes a DFS in $\tilde{O}(\sqrt{n})$…
Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…
Scientific programmers often turn to vendor-tuned Basic Linear Algebra Subprograms (BLAS) to obtain portable high performance. However, many numerical algorithms require several BLAS calls in sequence, and those successive calls result in…
We present an in-place depth first search (DFS) and an in-place breadth first search (BFS) that runs on a word RAM in linear time such that, if the adjacency arrays of the input graph are given in a sorted order, the input is restored after…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
Depth first search (DFS) tree is a fundamental data structure for solving various graph problems. The classical DFS algorithm requires $O(m+n)$ time for a graph having $n$ vertices and $m$ edges. In the streaming model, an algorithm is…