Kruskal Algorithm for minimum spanning..
- 2. Kruskal's Algorithm is used to find the minimum spanning tree for a connected weighted graph. The main target of the algorithm is to find the subset of edges by using which we can traverse every vertex of the graph. It follows the greedy approach that finds an optimum solution at every stage instead of focusing on a global optimum. # About Kruskal’s Algorithm
- 3. Spanning tree - A spanning tree is the subgraph of an undirected connected graph. Minimum Spanning tree - Minimum spanning tree can be defined as the spanning tree in which the sum of the weights of the edge is minimum. The weight of the spanning tree is the sum of the weights given to the edges of the spanning tree. Some Basic Terms Before Starting:
- 4. InKruskal's algorithm,westart fromedgeswiththelowest weightandkeepaddingtheedgesuntilthegoalis reached. Thesteps to implementKruskal's algorithmarelisted as follows - First, sort alltheedgesfromlowweighttohigh. Now ,take the edgewith the lowest weight andaddit tothespanningtree.If theedgetobeaddedcreatesa cycle,thenreject theedge. Continuetoaddtheedges untilwereachallvertices, anda minimumspanningtreeis created. Exampleof Kruskal’ s A lgorithm How Does Kruskal’s Algorithm works? Let’ s lookat howKruskal’ s approach functions using anexample.Using anexample,it willbe easier to comprehendKruskal’ s algorithm. Let’ s assumeaweightedgraphis –
- 5. 1.) Table after organizing the edges in the ascending order according to their weights :- Edge AB DE BC CD AE AC AD Weight 1 2 3 4 5 7 10
- 6. Phase 1– J oin the edge PQ having the weight 1to the MST. Phase 2 – J oin the edge ST having the weight 2 to the MST .Also,point to be noted that this is not making any cycle.
- 7. Phase 3 –Add the edge QR having the weight 3 to the MST Phase 4 – Select the edge RS having the weight 4 to the MST;also,you will notice that it is not composing the cycle
- 8. Phase 5 –Now, we will select the edge PT having the weight 5. Adding this edge will form the cycle, so we will dump it. Phase 6 –Pick the edge PR having the weight 7.Adding this edge will form the cycle,so we will dump it. Phase 7–Pick the edge PS having the weight 10.Adding this edge will form the cycle,so we will dump it.
- 9. Total value of MST is =PQ +ST +QR +RS =1+2 +3 +4 =1 0 . In the above tree,the number of edges now equals the number of vertices minus one.As a result,the algorithm has reached its conclusion. The final minimum spanning tree obtained from the given weighted graph by using Kruskal's algorithm
- 10. THE APPLICATIONS OF KRUSKAL’S ALGORITHM The technique by Kruskal can be used to build out electrical wiring across cities. It’s possible to operate it to set up LAN connections.
- 11. Group Members: • Shashwat Mishra 23BAI10448 • Dev Marwah 23BAI10310 • Dhanni Watti 23BCY10343 • Prateek Chhabra 23BAI10169 • Rajrup Roy Choudhury 23BAI10213 • Aryan Desai 23BAI10179
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