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When is Kruskal's algorithm commonly used in graph theory?

Question

When is Kruskal's algorithm commonly used in graph theory?

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Solution

Kruskal's algorithm is commonly used in graph theory when we need to find the minimum spanning tree (MST) of a connected, undirected graph. Here are the steps:

  1. Sort all the edges from low weight to high
  2. Start adding edges to the MST from the lowest weight edge, ensuring that no cycle is formed while adding the edge. If adding the edge creates a cycle, then reject this edge.
  3. Keep adding edges until all vertices are included in the MST.

The algorithm is named after Joseph Kruskal, who first described it in 1956. It is a greedy algorithm, meaning it makes the optimal choice at each step as it attempts to find the overall optimal way to solve the entire problem. This is why it always chooses the smallest edge to add next to the MST.

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Similar Questions

When is Kruskal's algorithm commonly used in graph theory?A) To find the shortest path between two nodesB) To find the minimum spanning tree of a connected, undirected graphC) To calculate the average distance between nodesD) To find the maximum flow in a graph

What is the time complexity of Kruskal’s algorithm?

Kruskal’s algorithm is used to ______Select one:a.find minimum spanning treeb.find single source shortest pathc.find all pair shortest path algorithmd.traverse the graph

How does Kruskal's algorithm find the minimum spanning tree in a graph?A) By selecting the edge with the smallest weightB) By selecting the edge with the largest weightC) By selecting edges randomlyD) By selecting edges based on a priority queu

Which is true statement in the followinga.Both of aboveb.Kruskal’s algorithm (choose best non-cycle edge) is better than prim’s(choose best tree edge) when the graph has relatively few edges.c.Kruskal’s algorithm is used to find MST of a graph , time complexity of this algorithm is O(EV)d.Kruskal’s algorithm is multiple source technique for finding MST.

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