Experimental analysis of dynamic algorithms for the single source shortest paths problem
Journal of Experimental Algorithmics (JEA)
Pattern matching in dynamic texts
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for Finding Noncrossing Steiner Forests in Plane Graphs
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Delta-Stepping: A Parallel Single Source Shortest Path Algorithm
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
All Pairs Shortest Paths in Undirected Graphs with Integer Weights
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Improved algorithm for all pairs shortest paths
Information Processing Letters
Geometric containers for efficient shortest-path computation
Journal of Experimental Algorithmics (JEA)
A note of an O(n3/logn) time algorithm for all pairs shortest paths
Information Processing Letters
Terracost: Computing least-cost-path surfaces for massive grid terrains
Journal of Experimental Algorithmics (JEA)
Geodesic Matting: A Framework for Fast Interactive Image and Video Segmentation and Matting
International Journal of Computer Vision
A faster algorithm for the single source shortest path problem with few distinct positive lengths
Journal of Discrete Algorithms
Improved algorithms for replacement paths problems in restricted graphs
Operations Research Letters
A Simple Implementation of Dijkstra's Shortest Path Algorithm on Associative Parallel Processors
Fundamenta Informaticae
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The single source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a weighted graph G with a source vertex s, find the shortest path from s to all other vertices in the graph. Since 1959 all theoretical developments in SSSP have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s. Thus, any implementation of Dijkstra's algorithm sorts the vertices according to their distances from s. However, we do not know how to sort in linear time. Here, a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with integer weights. The algorithm avoids the sorting bottle-neck by building a hierarchical bucketing structure, identifying vertex pairs that may be visited in any order.