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Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Dijkstra's algorithm finds the shortest path from a given source node to every other node. [7]: 196–206 It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of ...
A central problem in algorithmic graph theory is the shortest path problem. Hereby, the problem of finding the shortest path between every pair of nodes is known as all-pair-shortest-paths (APSP) problem. As sequential algorithms for this problem often yield long runtimes, parallelization has shown to be beneficial in this field. In this ...
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. [1] It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers. [2]
The Floyd–Warshall algorithm is an example of dynamic programming, and was published in its currently recognized form by Robert Floyd in 1962. [3] However, it is essentially the same as algorithms previously published by Bernard Roy in 1959 [4] and also by Stephen Warshall in 1962 [5] for finding the transitive closure of a graph, [6] and is closely related to Kleene's algorithm (published ...
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.
In graph theory, Yen's algorithm computes single-source K-shortest loopless paths for a graph with non-negative edge cost. [1] The algorithm was published by Jin Y. Yen in 1971 and employs any shortest path algorithm to find the best path, then proceeds to find K − 1 deviations of the best path.
The first three stages of Johnson's algorithm are depicted in the illustration below. The graph on the left of the illustration has two negative edges, but no negative cycles. The center graph shows the new vertex q, a shortest path tree as computed by the Bellman–Ford algorithm with q as starting vertex, and the values h(v) computed at each other node as the length of the shortest path from ...