Key point 2.5 Kruskal’s algorithm: Start to list the arcs in increasing order of weight. Step 1: Add an arc of minimum weight in such a way that no cycles are created. Step 2: If a spanning tree is obtained stop; otherwise return to Step 1.
Tip
WORKED EXAMPLE 2.2
PL E
Kruskal’s algorithm starts with the least weight arc and works through the arcs in increasing order of weight. It builds a collection of little trees that are eventually combined to make a single spanning tree.
M
Use Kruskal’s algorithm to find a minimum spanning tree for this network.
EH = 1
SA
CE = 2 EF = 2
Start by listing the arcs in order of increasing weight. Where there are arcs with the same weight they can appear in any order. It is not usually necessary to write out the whole list, but every vertex must be in the list.
EG = 2
BD = 3
GH = 3 AB = 5
…
✔
EH = 1
✔
C E = 2
Use Step 1 repeatedly to add arcs to the network (working down the list). Each time check that no cycles are created. Original material © Cambridge University Press 2018