The answer is no. To see why, let’s first articulate the question like so: Q: For a connected, undirected, weighted graph G = (V, E, w) with only nonnegative edge weights, does the predecessor subgraph produced by Dijkstra’s Algorithm form a minimum spanning tree of G? (Note that undirected graphs are a special class of … Read more
Prim’s algorithm constructs a minimum spanning tree for the graph, which is a tree that connects all nodes in the graph and has the least total cost among all trees that connect all the nodes. However, the length of a path between any two nodes in the MST might not be the shortest path between … Read more
There were algorithms called A1 and A2. Later, it was proved that A2 was optimal and in fact also the best algorithm possible, so he gave it the name A* which symbolically includes all possible version numbers. Source: In 1964 Nils Nilsson invented a heuristic based approach to increase the speed of Dijkstra’s algorithm. This … Read more
I’m the author of Grokking Algorithms. Sorry for this error—Dijkstra’s algorithm does work on graphs with cycles, as long as it is a positive weight cycle. I have updated the errata page to reflect this error. Dijkstra’s doesn’t work on negative weight cycles, and here’s an image that explains why:
As others have pointed out, Floyd-Warshall runs in time O(n3) and running a Dijkstra’s search from each node to each other node, assuming you’re using a Fibonacci heap to back your Dijkstra’s implementation, takes O(mn + n2 log n). However, you cannot always safely run Dijkstra’s on an arbitrary graph because Dijkstra’s algorithm does not … Read more
This is just some information I found while doing this in a class, that I shared with my classmates. I thought I’d make it easier for folks to find it, and I had left this post up so that I could answer it when I found a solution. Note: I’m assuming for this example that … Read more
It can be applied to both. Here is why: An undirected graph is basically the same as a directed graph with bidirectional connections (= two connections in opposite directions) between the connected nodes. So you don’t really have to do anything to make it work for an undirected graph. You only need to know all … Read more
As long as the graph does not contain a negative cycle (a directed cycle whose edge weights have a negative sum), it will have a shortest path between any two points, but Dijkstra’s algorithm is not designed to find them. The best-known algorithm for finding single-source shortest paths in a directed graph with negative edge … Read more
Disclaimer: I am the author and owner of OrientDB. As developer, in general, I don’t like companies that hide costs and let you play with their technology for a while and as soon as you’re tight with it, start asking for money. Actually once you invested months to develop your application that use a non … Read more
Breadth-first search is just Dijkstra’s algorithm with all edge weights equal to 1. Dijkstra’s algorithm is conceptually breadth-first search that respects edge costs. The process for exploring the graph is structurally the same in both cases.