Greedy approach

Given A T = MST(G), determine a safe edge (u,v) to add to A such that A {(u,v)} T

Greedy-MST(G,w)

A = {}

while A is not a spanning tree
; includes all vertices of G

find a safe edge (u,v) for A

A = A {(u,v)}

return A

What is a ``safe'' edge?

A safe edge is an edge connecting a vertex in A T to a vertex in G that is not in A such that A safe edge MST.