Revision - Minimum Connector Problems

The aim of minimum connector problems is to find the spanning tree of minimum weight.

Prim's algorithm

• Select any node the be the first node of the minimum spanning tree, T.
• Consider the arcs connecting the nodes currently in T to those outside of T. Pick the one of minimum weight. Add this arc and node to T.
• Repeat step 2 until all nodes are within T.

• Simple

• Time taken to check for smallest weight arc makes it slow for large numbers of nodes
• Difficult to program, though it can be programmed in matrix form.

Matrix formulation of Prim's algorithm

• Select any node to be the first node of T
• Circle the new node of T in the top row, and cross out the row corresponding to this new node.
• Find the smallest weight left in the columns with circled headings. Circle this weight. Then choose the node whose weight the row is in to join T.
• Repeat until T contains every node.

Kruskal's algorithm

For a graph with n nodes.

• Choose the arc of least weight
• From the remaining arcs, choose the one of least weight that does not form a cycle with already chosen arcs
• Repeat until n-1 arcs have been chosen