Bellman-Ford Shortest-Path Algorithm: Difference between revisions
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=Overview= | =Overview= | ||
A dynamic programming algorithm that can compute shortest path in graphs with [[Graph_Concepts#Negative_Length_Edge|negative length edges]]. The running time complexity is O(mn). | A dynamic programming algorithm that can compute shortest path in graphs with [[Graph_Concepts#Negative_Length_Edge|negative length edges]]. The running time complexity is O(mn): there are n<sup>2</sup> subproblems, and we might spend more than linear time for each subproblem: we have to do brute force search through a list of candidates that might be super-constant (each arc that comes into the vertex v provides a candidate for what the correct solution to the subproblem may be, and the number of candidates is proportional to the degree of vertex v). | ||
Revision as of 02:41, 30 November 2021
External
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/x0YZd/single-source-shortest-paths-revisted
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/g8N36/optimal-substructure
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/9YeyY/the-basic-algorithm-i
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/WhILJ/the-basic-algorithm-ii
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/AB5wH/detecting-negative-cycles
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/TrNPq/a-space-optimization
Internal
Overview
A dynamic programming algorithm that can compute shortest path in graphs with negative length edges. The running time complexity is O(mn): there are n2 subproblems, and we might spend more than linear time for each subproblem: we have to do brute force search through a list of candidates that might be super-constant (each arc that comes into the vertex v provides a candidate for what the correct solution to the subproblem may be, and the number of candidates is proportional to the degree of vertex v).