Kruskal Algorithm

Kruskal Algorithm

• 1.
  Kruskal AlgorithmKRUSKAL(V,E,W)A← ΦFor each vertex vЄG[v]Do MAKESET[v]sort E into nondecreasing order of weight wDo if FINDSET [u]≠FINDSET[v]A ← A U {(U,V)}UNION(U,V)Return (A)
• 2.
  88bcd249ai14711e33105fhgGiven: G isa connected undirected weighted graph 61
• 3.
  First sort theedges according to nondecreasing order of their weight
• 4.
  88bcd249ai14711e33105fhg61 (h,g) - weight 1 (c,f) - weight 7 ( c,i) - weight 2 (b,c) - weight 8 (i,h) - weight 3 (c,d) - weight 8 ( i,g) - weight 3 (d,e) - weight 9 (a,b) - weight 4 (e,f) -weight 10 (a,h) - weight 5 (d,f) - weight 11 (g,f) - weight 6 (b,h) weight 14
• 5.
  (h,g):Selectbcdaiefhg1
• 6.
  (c,i):Selectbcd2aiefhg1
• 7.
  Select(i,h):bcd2aie3fhg1
• 8.
  Reject(i,g):bcd2aie33fhg1
• 9.
  Select(a,b):bcd42aie3fhg1
• 10.
  Select(a,h):bcd24aie53fhg1
• 11.
  (g,f):Selectbcd42aie35fhg61
• 12.
  Reject(c,f):bcd24ai7e35fhg16
• 13.
  Select(c,d):8bcd24aie35fhg16
• 14.
  Reject(b,c):88bcd42aie35fhg16
• 15.
  Select(d,e):8bcd429aie35fhg16
• 16.
  Reject(e,f):8bcd429aie3510fhg16
• 17.
  Reject(d,f):8bcd429aie1135fhg16
• 18.
  Reject(b,h):8bcd429ai14e35fhg16
• 19.
  Minimum Spanning Tree8bcd429aie35fhg16Totalweight(MST)=1+2+3+4+5+6+8+9=38