Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
Communications of the ACM
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
General purpose parallel architectures
Handbook of theoretical computer science (vol. A)
A parallel randomized approximation scheme for shortest paths
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An introduction to parallel algorithms
An introduction to parallel algorithms
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Efficient parallel algorithms for computing all pair shortest paths in directed graphs
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Polylog-time and near-linear work approximation scheme for undirected shortest paths
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Efficient parallel shortest-paths in digraphs with a separator decomposition
Journal of Algorithms
Distributed computation on graphs: shortest path algorithms
Communications of the ACM
MPI: The Complete Reference
A Parallel Priority Data Structure with Applications
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
A Parallelization of Dijkstra's Shortest Path Algorithm
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Randomized parallel algorithms
Solving Combinatorial Optimization Problems in Parallel - Methods and Techniques
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Euro-Par '96 Proceedings of the Second International Euro-Par Conference on Parallel Processing - Volume I
A Simple Parallel Algorithm for the Single-Source Shortest Path Problem on Planar Digraphs
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
Undirected single source shortest paths in linear time
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Parallel tree contraction and its application
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Buckets Strike Back: Improved Parallel Shortest Paths
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Parallel Shortest Path for Arbitrary Graphs
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Heaps Are Better than Buckets: Parallel Shortest Paths on Unbalanced Graphs
Euro-Par '01 Proceedings of the 7th International Euro-Par Conference Manchester on Parallel Processing
CUDA Solutions for the SSSP Problem
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Synthesizing concurrent schedulers for irregular algorithms
Proceedings of the sixteenth international conference on Architectural support for programming languages and operating systems
MapReduce in MPI for Large-scale graph algorithms
Parallel Computing
Parallel computation of best connections in public transportation networks
Journal of Experimental Algorithmics (JEA)
Betweenness centrality: algorithms and implementations
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles
ACM SIGOPS 24th Symposium on Operating Systems Principles
A lightweight infrastructure for graph analytics
Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles
Distributed socialite: a datalog-based language for large-scale graph analysis
Proceedings of the VLDB Endowment
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In spite of intensive research, little progress has been made towards fast and work-efficient parallel algorithms for the single source shortest path problem. Our Δ-stepping algorithm, a generalization of Dial's algorithm and the Bellman-Ford algorithm, improves this situation at least in the following "average-case" sense: For random directed graphs with edge probability d/n and uniformly distributed edge weights a PRAM version works in expected time O(log3 n/ log log n) using linear work. The algorithm also allows for efficient adaptation to distributed memory machines. Implementations show that our approach works on real machines. As a side effect, we get a simple linear time sequential algorithm for a large class of not necessarily random directed graphs with random edge weights.