Shortest paths in Euclidean graphs
Algorithmica
Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
Communications of the ACM
Optimal and sublogarithmic time randomized parallel sorting algorithms
SIAM Journal on Computing
Fast and reliable parallel hashing
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
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
Randomized algorithms
Efficient parallel shortest-paths in digraphs with a separator decomposition
Journal of Algorithms
Random Geometric Problems on [0, 1]²
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Delta-Stepping: A Parallel Single Source Shortest Path Algorithm
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
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
Buckets Strike Back: Improved Parallel Shortest Paths
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
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
Distributed LTL Model Checking Based on Negative Cycle Detection
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
How to Employ Reverse Search in Distributed Single Source Shortest Paths
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
| Hi-index | 0.00 |
In spite of intensive research, no work-efficient parallel algorithm for the single source shortest path problem is known which works in sublinear time for arbitrary directed graphs with non-negative edge weights. We present an algorithm that improves this situation for graphs where the ratio dc/Δ between the maximum weight of a shortest path dc and a "safe step width" Δ is not too large. We show how such a step width can be found efficiently and give several graph classes which meet the above condition, such that our parallel shortest path algorithm runs in sublinear time and uses linear work.Th e new algorithm is even faster than a previous one which only works for random graphs with random edge weights [10]. On those graphs our new approach is faster by a factor of Θ(log n/ log log n) and achieves an expected time bound of O(log2 n) using linear work.