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Prim`s Algorithm

n In Lesson 1 we learnt about Kruskal`s algorithm,which was used to solve minimum connectorproblems.

n Another method that can be used is Prim`salgorithm.

n Step 1 Select any node

n Step 2 Connect it to the nearest node

n

Step 3 Connect one node already selected tothe nearest unconnected node.

n Step 4 Repeat 3 until all nodes are connected.

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Prim`s Algorithm

n Consider the example we looked at last lesson.

n Select any node you like.

n Lets select F.

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Prim`s Algorithm

n Connect it to the nearest node.

n C and D are both 3 away so we can choose either.

n Lets select C.

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Prim`s Algorithm

n The nearest node to either of F or C is D, which is only3 away from F.

n So connect D to F.

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Prim`s Algorithm

n The nearest to D, F or C is E which is 2 from D.

n So connect E to D.

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Prim`s Algorithm

n The nearest to any of these four nodes is A which is 5away from F.

n Connect A to F.

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Prim`s Algorithm

n We now need to connect the last node, B.

n The shortest arc is AB, which is 2.

n Connect B to A.

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Prim`s Algorithm

n All the nodes are now connected so this is theminimum connector or minimal spanning tree.

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Prim`s on a Distance Table

n We are going to apply Prim`s algorithm tothe distance table.

n This demonstrates how a computer could

apply the algorithm.n Prim`s is more suitable than Kruskal`s as

computers have a problem recognisingloops.

nAs you go through the algorithm, see if youcan relate the procedure to the last example.

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Prim`s on a Distance Table

n Step 1 Select any arbitrary node.

n Step 2 Delete the row and loop the columnthat correspond to the node selected.

n Step 3 Choose the smallest number in the loop.

n Step 4 Delete the row that this smallest number isin.

n Step 5 Loop the column that corresponds to therow just deleted.

n Step 6 Choose the smallest number in any loop.

n Step 7 Repeat steps 4, 5 and 6 until all rows havebeen deleted and columns looped.

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Prim`s on a Distance Table

n Here I have chosen F.

n Delete the row.

n Loop the column.

n Select the smallest number in the loop.

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Prim`s on a Distance Table

n Delete row C.

n Loop column C.

n Select the smallest number in any loop that is notcrossed out.

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Prim`s on a Distance Table

n Delete row D.

n Loop column D.

n Select the smallest number in any loop that is notcrossed out.

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Prim`s on a Distance Table

n Delete row E.

n Loop column E.

n Select the smallest number in any loop that is notcrossed out.

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Prim`s on a Distance Table

n Delete row A.

n Loop column A.

n Select the smallest number in any loop that is notcrossed out.

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Prim`s on a Distance Table

n Delete row B.

n Loop column B.

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Prim`s on a Distance Table

n The algorithm is complete when all the columns havebeen looped and the rows crossed out.

n The circles show the edges in the minimum connector.

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Prim`s on a Distance Table

n In this case they are AB, DE, AF, CF, DF

n Can you explain why this procedure is exactly the sameas applying Prim`s algorithm?