prim's spanning tree with Examples

1. PRIM’sSPANNINGTREEALGORITHM
Name : Anwar
Roll No : 44
MCS 3rd Open
TOPIC

2.  An algorithm is designed to achieve optimum solution for a given problem.
In greedy algorithm approach, decisions are made from the given solution
domain. As being greedy, the closest solution that seems to provide an
optimum solution is chosen.
 Greedy algorithms try to find a localized optimum solution, which may
eventually lead to globally optimized solutions. However, generally greedy
algorithms do not provide globally optimized solutions.
Greedy Algorithm Approach

3. s
 Most networking algorithms use the greedy approach. Here is a list of few of them −
 Travelling Salesman Problem
 Prim's Minimal Spanning Tree Algorithm
 Kruskal's Minimal Spanning Tree Algorithm
 Dijkstra's Minimal Spanning Tree Algorithm
 Graph - Map Coloring
 Graph - Vertex Cover
 Knapsack Problem
 Job Scheduling Problem
 There are lots of similar problems that uses the greedy approach to find an optimum solution.
Examples

4.  Example: Use Prim’s algorithm to find a minimum spanning tree in the following
weighted graph. Use alphabetical order to break ties.
B
A
2
Prim's Minimal Spanning Tree Algorithm

5.  Prim’s algorithm will proceed as follows. First we add edge {d, e} of weight1.
 Next, we add edge {c, e} of weight 2. Next, we add edge {d, z} of weight 2.
 Next, we add edge {b, e} of weight 3. And finally, we add edge {a, b} of
weight 2.
 This produces a minimum spanning tree of weight 10.
SOLUTION

6. minimumspanning tree is the following
AAAA
or

7. A minimumspanningtree
Tree
Vertices
 A(_,_)
 B(A,2)
 E(B,3)
 D(E,1)
 C(E,2)
 Z(D,2)
Remaining
Vertices
 B(A,2) C(A,3) D(_,_) E(_,_) Z(_,_)
 C(A,3) D(B,5) E(B,3) Z(_,_)
 C(E,2) D(E,1) Z(E,4)
 C(E,2) Z(D,2)
 Z(D,2)
ILLUSTRATION
minimum spanning tree

8. Add a Slide Title - 3
 Tree
Vertices
 A(_,_)
 B(A,2)
 C(A,3)
 E(C,2)
 D(E,1)
 Z(D,2)
 Remaining
Vertices
 B(A,2) C(A,3) D(_,_) E(_,_) Z(_,_)
 C(A,3) D(B,5) E(B,3) Z(_,_)
 D(B,5) E(C,2) Z(_,_)
 D(E,1) Z(E,4)
 Z(D,2)
ILLUSTRATION
minimum spanning tree