Search results
Results from the WOW.Com Content Network
A path in an undirected graph is a sequence of vertices = (,, ... Use a shortest path algorithm (e.g., Dijkstra's algorithm, Bellman-Ford algorithm) to find the ...
Dijkstra's algorithm is usually the working principle behind link-state routing protocols. OSPF and IS-IS are the most common. Unlike Dijkstra's algorithm, the Bellman–Ford algorithm can be used on graphs with negative edge weights, as long as the graph contains no negative cycle reachable from the source vertex s. The presence of such cycles ...
In connected graphs where shortest paths are well-defined (i.e. where there are no negative-length cycles), we may construct a shortest-path tree using the following algorithm: Compute dist(u), the shortest-path distance from root v to vertex u in G using Dijkstra's algorithm or Bellman–Ford algorithm.
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.
One way to do this is just run the Dijkstra algorithm. This takes time O ( m + n log n ) {\displaystyle O(m+n\log n)} , and requires no extra space (besides the graph itself). In order to answer many queries more efficiently, we can spend some time in pre-processing the graph and creating an auxiliary data structure.
Dijkstra's algorithm produces a list of shortest paths from a source vertex to every other vertex in directed and undirected graphs with non-negative edge weights (or no edge weights), whilst the Bellman–Ford algorithm can be applied to directed graphs with negative edge weights.
For the radius stepping algorithm, we must assume that our graph is undirected. The input to the algorithm is a weighted, undirected graph, a source vertex, and a target radius value for every vertex, given as a function r : V → R + {\displaystyle r:V\rightarrow \mathbb {R} _{+}} . [ 3 ]
In any graph, directed or undirected, there is a straightforward algorithm for finding a widest path once the weight of its minimum-weight edge is known: simply delete all smaller edges and search for any path among the remaining edges using breadth-first search or depth-first search.