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  2. Bellman–Ford algorithm - Wikipedia

    en.wikipedia.org/wiki/BellmanFord_algorithm

    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]

  3. File:Bellman-Ford worst-case example.svg - Wikipedia

    en.wikipedia.org/wiki/File:Bellman-Ford_worst...

    English: A worst-case example graph for Bellman-Ford algorithm, a simple path with 5 vertices. Assuming that the source is A and the edges are processed from right to left, it will take |V| - 1 or 4 iterations for the minimum distances (labelled below each node) to fully converge.

  4. 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 ...

  5. Bellman equation - Wikipedia

    en.wikipedia.org/wiki/Bellman_equation

    A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. [1] It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision ...

  6. Distance-vector routing protocol - Wikipedia

    en.wikipedia.org/wiki/Distance-vector_routing...

    Distance-vector routing protocols use the Bellman–Ford algorithm.In these protocols, each router does not possess information about the full network topology.It advertises its distance value (DV) calculated to other routers and receives similar advertisements from other routers unless changes are done in the local network or by neighbours (routers).

  7. Shortest path problem - Wikipedia

    en.wikipedia.org/wiki/Shortest_path_problem

    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.

  8. Dynamic programming - Wikipedia

    en.wikipedia.org/wiki/Dynamic_programming

    Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form. Bellman explains the reasoning behind the term dynamic programming in his autobiography, Eye of the Hurricane: An Autobiography: I spent the Fall quarter (of 1950) at RAND ...

  9. Shortest-path tree - Wikipedia

    en.wikipedia.org/wiki/Shortest-path_tree

    Example of one of two shortest-path trees where the root vertex is the red square vertex. The edges in the tree are indicated with green lines while the two dashed lines are edges in the full graph but not in the tree. The numbers beside the vertices indicate the distance from the root vertex.