Data Structures & Algorithms Multiple Choice Questions on “Maximum Bipartite Matching”.
1. _____________ is a matching with the largest number of edges. Answer: a 2. Maximum matching is also called as maximum cardinality matching. Answer: a 3. How many colours are used in a bipartite graph? 4. What is the simplest method to prove that a graph is bipartite? Answer: c 5. A matching that matches all the vertices of a graph is called? Answer: a 6. What is the length of an augmenting path? Answer: b 7. In a bipartite graph G=(V,U,E), the matching of a free vertex in V to a free vertex in U is called? Answer: c 8. A matching M is maximal if and only if there exists no augmenting path with respect to M. Answer: a 9. Which one of the following is an application for matching? Answer: b 10. Which is the correct technique for finding a maximum matching in a graph? Answer: b 11. The problem of maximizing the sum of weights on edges connecting matched pairs of vertices is? Answer: c 12. What is the total number of iterations used in a maximum- matching algorithm? Answer: d 13. What is the efficiency of algorithm designed by Hopcroft and Karp? 14. Who was the first person to solve the maximum matching problem? 15. From the given graph, how many vertices can be matched using maximum matching in bipartite graph algorithm? Answer: a
a) Maximum bipartite matching
b) Non-bipartite matching
c) Stable marriage
d) Simplex
Clarification: Maximum bipartite matching matches two elements with a property that no two edges share a vertex.
a) True
b) False
Clarification: Maximum matching is also called as maximum cardinality matching (i.e.) matching with the largest number of edges.
a) 1
b) 2
c) 3
d) 4
Answer: b
Clarification: A bipartite graph is said to be two-colourable so that every edge has its vertices coloured in different colours.
a) It has a cycle of an odd length
b) It does not have cycles
c) It does not have a cycle of an odd length
d) Both odd and even cycles are formed
Clarification: It is not difficult to prove that a graph is bipartite if and only if it does not have a cycle of an odd length.
a) Perfect matching
b) Cardinality matching
c) Good matching
d) Simplex matching
Clarification: A matching that matches all the vertices of a graph is called perfect matching.
a) Even
b) Odd
c) Depends on graph
d) 1
Clarification: The length of an augmenting path in a bipartite graph is always said to be always odd.
a) Bipartite matching
b) Cardinality matching
c) Augmenting
d) Weight matching
Clarification: A simple path from a free vertex in V to a free vertex in U whose edges alternate between edges not in M and edges in M is called a augmenting path.
a) True
b) False
Clarification: According to the theorem discovered by the French mathematician Claude Berge, it means that the current matching is maximal if there is no augmenting path.
a) Proposal of marriage
b) Pairing boys and girls for a dance
c) Arranging elements in a set
d) Finding the shortest traversal path
View Answer
Clarification: Pairing boys and girls for a dance is a traditional example for matching. Proposal of marriage is an application of stable marriage problem.
a) DFS traversal
b) BFS traversal
c) Shortest path traversal
d) Heap order traversal
Clarification: The correct technique for finding a maximum matching in a bipartite graph is by using a Breadth First Search(BFS).
a) Maximum- mass matching
b) Maximum bipartite matching
c) Maximum weight matching
d) Maximum node matching
Clarification: The problem is called as maximum weight matching which is similar to a bipartite matching. It is also called as assignment problem.
a) [n/2]
b) [n/3]
c) [n/2]+n
d) [n/2]+1
Clarification: The total number of iterations cannot exceed [n/2]+1 where n=|V|+|U| denoting the number of vertices in the graph.
a) O(n+m)
b) O(n(n+m)
c) O(√n(n+m))
d) O(n+2)
Answer: c
Clarification: The efficiency of algorithm designed by Hopcroft and Karp is mathematically found to be O(√n(n+m)).
a) Jack Edmonds
b) Hopcroft
c) Karp
d) Claude Berge
Answer: a
Clarification: Jack Edmonds was the first person to solve the maximum matching problem in 1965.
a) 5
b) 4
c) 3
d) 2
View Answer
Clarification: One of the solutions of the matching problem is given by a-w,b-v,c-x,d-y,e-z. Hence the answer is 5.