Related papers: More Parallelism in Dijkstra's Single-Source Short…
All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…
We give the first parallel algorithm with optimal $\tilde{O}(m)$ work for the classical problem of computing Single-Source Shortest Paths in general graphs with negative-weight edges. In graphs without negative edges, Dijkstra's algorithm…
The single-source shortest path problem (SSSP) with nonnegative edge weights is a notoriously difficult problem to solve efficiently in parallel---it is one of the graph problems said to suffer from the transitive-closure bottleneck. In…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different…
We present an implementation and experimental analysis of the deterministic algorithm proposed by Duan et al. (2025) for the Single-Source Shortest Path (SSSP) problem, which achieves the best-known asymptotic upper bound of $O(m \log^{2/3}…
The single-source shortest path (SSSP) problem is a well-studied problem that is used in many applications. In the parallel setting, a work-efficient algorithm that additionally attains $o(n)$ parallel depth has been elusive. Alternatively,…
We describe a new forward-backward variant of Dijkstra's and Spira's Single-Source Shortest Paths (SSSP) algorithms. While essentially all SSSP algorithm only scan edges forward, the new algorithm scans some edges backward. The new…
In this paper, we study the single-source shortest-path (SSSP) problem with positive edge weights, which is a notoriously hard problem in the parallel context. In practice, the $\Delta$-stepping algorithm proposed by Meyer and Sanders has…
Utilizing graph algorithms is a common activity in computer science. Algorithms that perform computations on large graphs are not always efficient. This work investigates the Single-Source Shortest Path (SSSP) problem, which is considered…
This paper investigates the parallelization of Dijkstra's algorithm for computing the shortest paths in large-scale graphs using MPI and CUDA. The primary hypothesis is that by leveraging parallel computing, the computation time can be…
The Single-Source Shortest Path (SSSP) problem is a cornerstone of computer science with vast applications, for which Dijkstra's algorithm has long been the classical baseline. While various quantum algorithms have been proposed, their…
We study the use of machine learning techniques to solve a fundamental shortest path problem, known as the single-source many-targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to…
Images conveniently capture the result of physical processes, representing rich source of information for data driven medicine, engineering, and science. The modeling of an image as a graph allows the application of graph-based algorithms…
We present parallel algorithms for computing single-source reachability and shortest paths on directed $n$-vertex $m$-edge graphs using near-linear $\tilde{O}(m)$ work and $o(\sqrt{n})$ depth whenever $m\ge n^{1+o(1)}$. At the extreme of…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
Modern graphs are both large and dynamic, presenting significant challenges for fundamental queries, such as the Single-Source Shortest Path (SSSP) problem. Naively recomputing the SSSP tree after each topology change is prohibitively…
In this paper, we show new strongly polynomial work-depth tradeoffs for computing single-source shortest paths (SSSP) in non-negatively weighted directed graphs in parallel. Most importantly, we prove that directed SSSP can be solved within…
We present a shared memory implementation of a parallel algorithm, called delta-stepping, for solving the single source shortest path problem for directed and undirected graphs. In order to reduce synchronization costs we make some…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…