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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.
Dykstra's algorithm is a method that computes a point in the intersection of convex sets, and is a variant of the alternating projection method (also called the projections onto convex sets method).
Compute dist(u), the shortest-path distance from root v to vertex u in G using Dijkstra's algorithm or Bellman–Ford algorithm. For all non-root vertices u , we can assign to u a parent vertex p u such that p u is connected to u , and that dist( p u ) + edge_dist( p u , u ) = dist( u ).
These algorithms are based on two different principles, either performing a shortest path algorithm such as Dijkstra's algorithm on a visibility graph derived from the obstacles or (in an approach called the continuous Dijkstra method) propagating a wavefront from one of the points until it meets the other.
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.
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 k shortest path routing problem is a generalization of the shortest path routing problem in a given network. It asks not only about a shortest path but also about next k−1 shortest paths (which may be longer than the shortest path).
Dijkstra's algorithm fails if there is a negative edge weight. In the hypothetical situation where Nodes A, B, and C form a connected undirected graph with edges AB = 3, AC = 4, and BC = −2, the optimal path from A to C costs 1, and the optimal path from A to B costs 2.