Further Maths - Kruskal's Algorithm

Pearson Edexcel Further Mathematics 2022


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Flashcards

Spanning trees

What is a spanning tree?

A tree that includes all the vertices of a graph.

What is a minimum spanning tree?

A tree that includes all the vertices of a graph at the minimum possible cost.

The steps of Kruskal’s algorithm

What is the first step of Kruskal’s algorithm?

List the edges in the order of weight, smallest first.

What step comes after listing out the edges of a graph in weight order for Kruskal’s algorithm?

Repeatedly choosing the edge with the smallest weight as long as it does not form a with already chosen edges.

Counting edges in a minimum spanning tree

How many edges do you need to create a minimum spanning tree for $7$ vertices?

\[6\]

How many edges do you need to create a minimum spanning tree for $69$ vertices?

\[68\]

Greedy algorithms and complexity

What is a greedy algorithm?

One that makes locally optimal choices without considering the context.

Why is Kruskal’s algorithm greedy?

Because it chooses the best edge available at every stage.

What is the complexity of Kruskal’s algorithm?

\[O(n^3)\]