Lecture 3 - Prim-Jarnik Algorithm

Question 1

What kind of an algorithm is the prim-jarnik algorithm?

Answer 1

A greey algorithm, it makes decisions based on local optimality in order to get a globally optimal solution.

Question 2

What is the complexity of this algorithm?

Answer 2

O(n^3)

• initialisation of vertices into ntvs and tvs is O(n)
• Outer while loop is executed n-1 times, this is O(n)
• Inner loop goes through all edges between vertices, there can be n^2 of these, so O(n^2)
• updating tree is O(1)

Question 3

What is a tv ?

Answer 3

tree vertex

Question 4

What is an ntv?

Answer 4

non- tree vertex

Question 5

How does the algorithm work?

Answer 5

• set one vertex to be a tv
• set all other vertices to be ntvs
• until all vertices are tvs
  find smallest edge from tv to ntv
  mark edge , add weight
  add that ntv to tvs