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  2. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    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.

  3. Dijkstra's algorithm - Wikipedia

    en.wikipedia.org/wiki/Dijkstra's_algorithm

    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 ...

  4. Shortest-path graph - Wikipedia

    en.wikipedia.org/wiki/Shortest-path_graph

    The shortest-path graph with t = 2. In mathematics and geographic information science, a shortest-path graph is an undirected graph defined from a set of points in the Euclidean plane. The shortest-path graph is proposed with the idea of inferring edges between a point set such that the shortest path taken over the inferred edges will roughly ...

  5. A* search algorithm - Wikipedia

    en.wikipedia.org/wiki/A*_search_algorithm

    Given a weighted graph, a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from source to goal. One major practical drawback is its O ( b d ) {\displaystyle O(b^{d})} space complexity where d is the depth of the solution (the length of the shortest path) and b is the branching factor (the ...

  6. Parallel single-source shortest path algorithm - Wikipedia

    en.wikipedia.org/wiki/Parallel_single-source...

    A central problem in algorithmic graph theory is the shortest path problem.One of the generalizations of the shortest path problem is known as the single-source-shortest-paths (SSSP) problem, which consists of finding the shortest paths from a source vertex to all other vertices in the graph.

  7. Yen's algorithm - Wikipedia

    en.wikipedia.org/wiki/Yen's_algorithm

    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.

  8. Johnson's algorithm - Wikipedia

    en.wikipedia.org/wiki/Johnson's_algorithm

    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 ...

  9. Shortest-path tree - Wikipedia

    en.wikipedia.org/wiki/Shortest-path_tree

    In graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. For simple connected graphs, shortest-path trees can be used [1] to suggest a non-linear relationship between two network centrality measures, closeness and degree. By assuming that the branches of the shortest-path ...