o8: (5 marks) the maximum-matching algorithm to the following bipartite graph: Apply 2 8 9 10
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Q. No. 1: (a) Starting with the matching Ma - ((1, 5)}, apply the maximum-matching algorithm to the following bipartite graph: Solution (b) Is it a perfect matching? Solution:
Q. No. 1: (a) Starting with the matching Ma - ((1, 5)}, apply the maximum-matching algorithm to the following bipartite graph: Solution (b) Is it a perfect matching? Solution:
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(3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of G.)
(3) Prove that for a bipartite graph G on n vertices, we have a(G)- n/2 if and only if G has a perfect matching. (Recall that α(G) is the maximum size among the independent subsets of...
Apply the selection algorithm to the sequence 9, 12, 5, 17, 20,
30, 8 to find the median. Show the steps of the algorithm in a
manner similar to the example shown below for organization(this is
not a solution, it is just provided as an example).
41108712 9 215 41108712 9 2 15 41108712 9 2 15 4128712 9 10 15 4128712 9 10 15 2148712 9 10 15 8 5 22 77 2 ils S1 0 42
Problem 8. (2+4+4 points each) A bipartite graph G = (V. E) is a graph whose vertices can be partitioned into two (disjoint) sets V1 and V2, such that every edge joins a vertex in V1 with a vertex in V2. This means no edges are within V1 or V2 (or symbolically: Vu, v E V1. {u, u} &E and Vu, v E V2.{u,v} &E). 8(a) Show that the complete graph K, is a bipartite graph. 8(b) Prove that no...
Question 9. Prove that if M' is a maximal matching and M is a maximum matching in a graph G, then AMM /2.
Question 5 (5 points) Apply Dijkstra's Algorithm to the following graph, computing the shortest path for al vertices from vertex A. Present the results after each vertex has been processed 3 20 B 47 20 You may wish to present the results in the format of the following table: Stage Current Vertex Labels and Distances A 0 A 0 D 231 A 213 E 4 F21 A 90 Each row states (a) the current stage, (b) the vertex just added...
• Apply the MAX-HEAPIFY algorithm to the following array A on node i = 2 and give the resulting array. | i Ali | 1 | 2 | 3 | 4 | 5 6 | 7 | 8 | 9 | 10 81 19 76 62 54 63 66 38 43 22 Answer: 1 2 3 4 5 6 7 8 9 10 Ai
Question 3 Apply Kruskal's algorithm to find Minimum Spanning Tree for the following graph. (In the final exam, you might be asked about Prim's algorithm or both). Weight of edge(1,2) = 10 Weight of edge(2,4)= 5 Weight of edge(6,4)=10 Weight of edge(1,4) = 20 Weight of edge(2,3) = 3 Weight of edge(6,5)= 3 Weight of edge(1,6) = 2 Weight of edge(3,5) = 15 Weight of edge(4,5)= 11
3. Apply Topological sort algorithm on the following graph. Then, draw the sorted graph. 11 marvel
5. Apply Dijkstra's algorithm as discussed in class to solve the single-source shortest-paths problem for the following graph. Consider node A to be the source. (20 points) a. Show the completed table. b. State the shortest path from A to E and state its length. C. State the shortest path from A to F and state its length. d. State the shortest path from A to G and state its length. A 12 9 B 17 8 7 10 8...