The Minimum Connector Problem: Finding the shortest way to link all the vertices in a graph. Method: Find a minimum spanning tree An example would be joining up several towns with an oil pipeline. Each town does not have to be joined to every other but they all have to be joined into the pipe line.

NorwichYarmouthLowestoftBeccles Norwich Yarmouth Lowestoft Beccles Using Prim`s Algorithm if the data is in a chart/matrix Find the minimum length of telephone cable required to join up the exchanges in the towns.

Choose any column vertex and delete the row corresponding to this vertex Circle the chosen vertex i.e. choose Yarmouth column - delete Yarmouth row NorwichYarmouthLowestoftBeccles Norwich Yarmouth Lowestoft Beccles

Ring the smallest entry in the column corresponding to this vertex i.e. 8 mls to Lowestoft in the Yarmouth column. Ring it. Delete the Lowestoft row and circle the Lowestoft column. NorwichYarmouthLowestoftBeccles Norwich Yarmouth Lowestoft Beccles Y 8 L

Look for the smallest entry in the columns corresponding to these 2 vertices i.e. the Yarmouth and Lowestoft column 10 is the smallest in the Beccles row. Ring it. Delete the Beccles row and circle the Beccles column. NorwichYarmouthLowestoftBeccles Norwich Yarmouth Lowestoft Beccles Y B 8 L Y 8 L

Look for the smallest entry in the columns corresponding to these 3 vertices i.e. the Yarmouth, Lowestoft and Beccles column. 15 is the smallest in the Norwich row. Ring it NorwichYarmouthLowestoftBeccles Norwich Yarmouth Lowestoft Beccles Y B 8 L Y 15 B 10 8 L N The minimum length of cable = 33mls