prim's Algorithm

1. Prim’s Algorithm
By : Garishma Bhatia

2. Content Layout List
• Minimal Spanning Tree
• Prim’s Algorithm
• Example
• Algorithm
• Analysis
• Complexity

3. Minimum Spanning Tree?
• A spanning tree is a subset of Graph G, which has all the vertices
covered with minimum possible number of edges.
• Hence, a spanning tree does not have cycles and it cannot be
disconnected.

4. Prim’s Algorithm
• Prim's algorithm is a greedy algorithm that finds a minimum spanning
tree for a weighted undirected graph.
• The algorithm was developed in 1930.

5. Algorithm
1. Prim(G,W)
2. VT = {v}
3. ET ={ ø }
4. For i=1 to |v|-1
5. Select an edge with minimum weight
6. e*=(u*,v*),such that u*€ VT & V* € V-VT, such
that inclusion of that edge does not forms a
cycle.
7. VT = VT U{V*}
8. ET = ET U{e*}
9. return ET

6. Example
v1
v2
v5
v7
v4v6
v3
3
1
4
2
9
2
7
4 8 4
36
V={V1,V2,V3,V4,V5,V6,V7}
VT={EMPTY}

7. v2
v2
v3
2
v
V={V1,V2,V3,V4,V5,V6,V7}
VT={V2}
V={V1,V2,V3,V4,V5,V6,V7}
VT={V2,V3}

8. v1
v2
v3
3 2
V={V1,V2,V3,V4,V5,V6,V7}
VT={V2,V3,V1}

9. v1
v2
v6
v3
3
1
2
V={V1,V2,V3,V4,V5,V6,V7}
VT={V2,V3,V1,V6}

10. v1
v2
v7
v6
v3
3
1
4
2
V={V1,V2,V3,V4,V5,V6,V7}
VT={V2,V3,V1,V6,V7}

11. v1
v2
v5
v7
v6
v3
3
1
4
2
2 V={V1,V2,V3,V4,V5,V6,V7}
VT={V2,V3,V1,V6,V7,V5}

12. v1
v2
v5
v7
v4v6
v3
3
1
4
2
2
3
V={V1,V2,V3,V4,V5,V6,V7}
VT={V2,V3,V1,V6,V7,V5,V4}

13. Analysis
T(V,E) = C+(V-1)[log E +C]
Complexity
T(V,E) € (V.log E)
1. Prim(G,W)
2. VT = { ø v} ------------------------------- C
3. ET ={ ø } ----------------------------------C
4. For i=1 to |v|-1 -----------------------(V-1)
5. { Select an edge with minimum weight
6. e*=(u*,v*),such that u*€ VT & V* € V-VT, such that
inclusion of that edge does not forms a cycle. } ---
------------------------------(log E)
7. VT = VT U{V*} -------------------------C
8. ET = ET U{e*} ---------------------------C
9. return ET --------------------------------------------- C

14. Thank You