Kruskals algorithm, Data Structure & Algorithms

Assignment Help:

Krushkal's algorithm uses the concept of forest of trees. At first the forest contains n single node trees (and no edges). At each of the step, we add on one (the cheapest one) edge so that it links two trees together. If it makes a cycle, simply it would mean that it links two nodes that were connected already. So, we reject it.

The steps in Kruskal's Algorithm are as:

1.   The forest is constructed through the graph G - along each node as a separate tree in the forest.

2.   The edges are placed within a priority queue.

3.   Do till we have added n-1 edges to the graph,

  I.   Extract the lowest cost edge from the queue.

 II.   If it makes a cycle, then a link already exists among the concerned nodes. So reject it.

 III.  Otherwise add it to the forest. Adding it to the forest will join two trees together.

The forest of trees is a division of the original set of nodes. At first all the trees have exactly one node in them. As the algorithm progresses, we make a union of two of the trees (sub-sets), until the partition has only one sub-set containing all the nodes eventually.

Let us see the sequence of operations to determine the Minimum Cost Spanning Tree(MST) in a graph via Kruskal's algorithm. Suppose the graph of graph shown in figure  and below figure  illustrates the construction of MST of graph of Figure

1339_Kruskals Algorithm.png

Figure: A Graph

Figure: Construction of Minimum Cost Spanning Tree for the Graph by application of Kruskal's algorithm

The following are several steps in the construction of MST for the graph of Figure via Kruskal's algorithm.

Step 1 :  The lowest cost edge is chosen from the graph that is not in MST (initially MST is empty). The cheapest edge is 3 that is added to the MST (illustrated in bold edges)

Step 2: The next cheap edge which is not in MST is added (edge with cost 4).

Step 3 : The next lowest cost edge that is not in MST is added (edge with cost 6).

 Step 4 : The next lowest cost edge that is not in MST is added (edge with cost 7).

Step 5 : The next lowest cost edge that is not in MST is 8 but form a cycle. Hence, it is discarded. The next lowest cost edge 9 is added. Now the MST has all the vertices of the graph. This results in the MST of the original graph.


Related Discussions:- Kruskals algorithm

Explain stacks, What are stacks? A stack is a data structure that organ...

What are stacks? A stack is a data structure that organizes data similar to how one organizes a pile of coins. The new coin is always placed on the top and the oldest is on the

Explain arrays, Arrays :- To execute a stack we need a variable called top,...

Arrays :- To execute a stack we need a variable called top, that holds the index of the top element of stack and an array to hold the part of the stack.

Basic organization of computer system, what happen''s in my computer when ...

what happen''s in my computer when i input any passage

Which sorting algorithms not have running time of o (n2), Which sorting al...

Which sorting algorithms does not have a worst case running time of  O (n 2 ) ? Merge sort

Binary tree and binarytree parts, Q. What do you understand by the term Bin...

Q. What do you understand by the term Binary Tree? What is the maximum number of nodes which are possible in a Binary Tree of depth d. Explain the terms given below with respect to

Pest control program, PART- Pest Control Program Prepare a Pest Contro...

PART- Pest Control Program Prepare a Pest Control Program for the facility that will address the management of Rodents, Insects and Birds. Your Pest Control Program should

Surrounding of sub division method, Surrounding of sub division method ...

Surrounding of sub division method A polygon surrounds a viewport if it completely encloses or covers the viewport. This happens if none of its sides cuts any edge of the viewp

Maximum numbers of nodes a binary tree of depth d, Maximum numbers of nodes...

Maximum numbers of nodes a binary tree of depth d The maximum numbers of nodes a binary tree of depth d can have is 2 d+1 -1.

Tree, application of threaded binary treee

application of threaded binary treee

Dynamic memory management, How memory is freed using Boundary tag method in...

How memory is freed using Boundary tag method in the context of Dynamic memory management? Boundary Tag Method to free Memory To delete an arbitrary block from the free li

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd