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Dijkstra's algorithm (/ ˈ d aɪ k s t r ə z / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.
Find the Shortest Path: Use a shortest path algorithm (e.g., Dijkstra's algorithm, Bellman-Ford algorithm) to find the shortest path from the source node to the sink node in the residual graph. Augment the Flow: Find the minimum capacity along the shortest path. Increase the flow on the edges of the shortest path by this minimum capacity.
This field of research is based heavily on Dijkstra's algorithm for finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem , within graph theory , which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest, etc) between two points in a large network.
The Dijkstra algorithm originally was proposed as a solver for the single-source-shortest-paths problem. However, the algorithm can easily be used for solving the All-Pair-Shortest-Paths problem by executing the Single-Source variant with each node in the role of the root node. In pseudocode such an implementation could look as follows:
Construct the shortest-path tree using the edges between each node and its parent. The above algorithm guarantees the existence of shortest-path trees. Like minimum spanning trees, shortest-path trees in general are not unique. In graphs for which all edge weights are equal, shortest path trees coincide with breadth-first search trees. In ...
There are classical sequential algorithms which solve this problem, such as Dijkstra's algorithm. In this article, however, we present two parallel algorithms solving this problem. Another variation of the problem is the all-pairs-shortest-paths (APSP) problem, which also has parallel approaches: Parallel all-pairs shortest path algorithm.
The shortest path in a graph can be computed using Dijkstra's algorithm but, given that road networks consist of tens of millions of vertices, this is impractical. [1] Contraction hierarchies is a speed-up method optimized to exploit properties of graphs representing road networks. [2] The speed-up is achieved by creating shortcuts in a ...
There are many results on computing shortest paths which stays on a polyhedral surface. Given two points s and t, say on the surface of a convex polyhedron, the problem is to compute a shortest path that never leaves the surface and connects s with t. This is a generalization of the problem from 2-dimension but it is much easier than the 3 ...