Question

can any one plz help me how to Find the MST using the PRIM algorithm. Highlight the edges of the MST and write the sequence in which the nodes are added to the MST..
thanks

Answer 1

Quoting The Directed Minimum Spanning Tree Problem:

1. Discard the arcs entering the root if any; For each node other than the
   root, select the entering arc with the
   smallest cost; Let the selected n-1
   arcs be the set S.
2. If no cycle formed, G(N,S) is a MST. Otherwise, continue.
3. For each cycle formed, contract the nodes in the cycle into a pseudo-node
   (k), and modify the cost of each arc
   which enters a node (j) in the cycle
   from some node (i) outside the cycle
   according to the following equation.
   c(i,k)=c(i,j)-(c(x(j),j)-min_{j}(c(x(j),j))
   here c(x(j),j) is the cost of the arc
   in the cycle which enters j.
4. For each pseudo-node, select the entering arc which has the smallest
   modified cost; Replace the arc which
   enters the same real node in S by the
   new selected arc.
5. Go to step 2 with the contracted graph.

The key idea of the algorithm is to
find the replacing arc(s) which has
the minimum extra cost to eliminate
cycle(s) if any. The given equation
exhibits the associated extra cost.