- Graph and its representations
- Greedy Algorithms | Set 5 (Prim’s Minimum Spanning Tree (MST))
- Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2
Given a directed graph D = < V, E >, the task is to find the minimum spanning tree for the given directed graph
Why Prim’s Algorithm Fails for Directed Graph ?
As it is visible in the graph, no node is reachable from node 4. Directed graphs fail the requirement that all vertices are connected.
Why Kruskal’s Algorithm fails for directed graph ?
In Kruskal’s algorithm, In each step, it is checked that if the edges form a cycle with the spanning-tree formed so far. But Kruskal’s algorithm fails to detect the cycles in a directed graph as there are cases when there is no cycle between the vertices but Kruskal’s Algorithm assumes it to cycle and don’t take consider some edges due to which Kruskal’s Algorithm fails for directed graph.
This graph will be reported to contain a cycle with the Union-Find method, but this graph has no cycle.
The equivalent of minimum spanning tree in directed graphs is, “Minimum Spanning Arborescence”(also known as optimum branching) can be solved by Edmonds’ algorithm with a running time of O(EV). This algorithm is directed analog of the minimum spanning tree problem.
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- Hierholzer's Algorithm for directed graph
- Convert the undirected graph into directed graph such that there is no path of length greater than 1
- Convert undirected connected graph to strongly connected directed graph
- Check if a directed graph is connected or not
- Detect Cycle in a Directed Graph using BFS
- Convert Directed Graph into a Tree
- Detect Cycle in a Directed Graph
- Euler Circuit in a Directed Graph
- Clone a Directed Acyclic Graph
- Shortest Path in Directed Acyclic Graph
- Detect Cycle in a directed graph using colors
- Longest Path in a Directed Acyclic Graph
- Find if there is a path between two vertices in a directed graph
- Path with minimum XOR sum of edges in a directed graph
- Longest Path in a Directed Acyclic Graph | Set 2
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