Give pseudocode to implement a phase of Boruvka’s algorithm. Argue that ˙ the running time of...

Give pseudocode to implement a phase of Boruvka’s algorithm. Argue that ˙ the running time of your implementation is O(m)

Expert Solution

Boruvka's Algorithm:

initialise with vertices as individual blue tree
for every blue tree, colour the cheapest edge leaving each tree as blue
repeat until a single blue tree
output all blue edges

The second step of the algorithm is Boruvka's phase.

Pseudocode to implement a Boruvka's phase:

Assume the graph is given as adjacency list.

given the adjacency list of , run through the list of edges incident to each vertex, to find the cheapest one.

Time complexity of Boruvka's phase:

For each vertex we spend time to search the cheapest edge incident on it.

Therefore, total time taken by one phase of Boruvka's algorithm is the sum of degrees of the vertices, i.e.

.

venereology answered 3 hours ago

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