This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Minimum Cut”.

1. Which algorithm is used to solve a minimum cut algorithm?

a) Gale-Shapley algorithm

b) Ford-Fulkerson algorithm

c) Stoer-Wagner algorithm

d) Prim’s algorithm

View Answer

Explanation: Minimum cut algorithm is solved using Stoer-Wagner algorithm. Maximum flow problem is solved using Ford-Fulkerson algorithm. Stable marriage problem is solved using Gale-Shapley algorithm.

2. ___________ is a partition of the vertices of a graph in two disjoint subsets that are joined by atleast one edge.

a) Minimum cut

b) Maximum flow

c) Maximum cut

d) Graph cut

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Explanation: Minimum cut is a partition of the vertices in a graph 4. in two disjoint subsets joined by one edge. It is a cut that is minimal in some sense.

3. Minimum cut algorithm comes along with the maximum flow problem.

a) true

b) false

View Answer

Explanation: Minimum cut algorithm is considered to be an extension of the maximum flow problem. Minimum cut is finding a cut that is minimal.

4. What does the given figure depict?

a) min cut problem

b) max cut problem

c) maximum flow problem

d) flow graph

View Answer

Explanation: The given figure is a depiction of min cut problem since the graph is partitioned to find the minimum cut.

5. ______________ separates a particular pair of vertices in a graph.

a) line

b) arc

c) cut

d) flow

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Explanation: A cut separates a particular pair of vertices in a weighted undirected graph and has minimum possible weight.

6. What is the minimum number of cuts that a graph with ‘n’ vertices can have?

a) n+1

b) n(n-1)

c) n(n+1)/2

d) n(n-1)/2

View Answer

Explanation: The mathematical formula for a graph with ‘n’ vertices can at the most have n(n-1)/2 distinct vertices.

7. What is the running time of Karger’s algorithm to find the minimum cut in a graph?

a) O(E)

b) O(|V|^{2})

c) O(V)

d) O(|E|)

View Answer

Explanation: The running time of Karger’s algorithm to find the minimum cut is mathematically found to be O(|V|

^{2}).

8. _____________ is a family of combinatorial optimization problems in which a graph is partitioned into two or more parts with constraints.

a) numerical problems

b) graph partition

c) network problems

d) combinatorial problems

View Answer

Explanation: Graph partition is a problem in which the graph is partitioned into two or more parts with additional conditions.

9. The weight of the cut is not equal to the maximum flow in a network.

a) true

b) false

View Answer

Explanation: According to max-flow min-cut theorem, the weight of the cut is equal to the maximum flow that is sent from source to sink.

10. __________ is a data structure used to collect a system of cuts for solving min-cut problem.

a) Gomory-Hu tree

b) Gomory-Hu graph

c) Dancing tree

d) AA tree

View Answer

Explanation: Gomory-Hu tree is a weighted tree that contains the minimum cuts for all pairs in a graph. It is constructed in |V|-1 max-flow computations.

11. In how many ways can a Gomory-Hu tree be implemented?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: Gomory-Hu tree can be implemented in two ways- sequential and parallel.

12. The running time of implementing naïve solution to min-cut problem is?

a) O(N)

b) O(N log N)

c) O(log N)

d) O(N^{2})

View Answer

Explanation: The running time of min-cut algorithm using naïve implementation is mathematically found to be O(N

^{2}).

13. What is the running time of implementing a min-cut algorithm using bidirected edges in a graph?

a) O(N)

b) O(N log N)

c) O(N^{4})

d) O(N^{2})

View Answer

Explanation: The running time of a min-cut algorithm using Ford-Fulkerson method of making edges birected in a graph is mathematically found to be O(N

^{4}).

14. Which one of the following is not an application of max-flow min-cut algorithm?

a) network reliability

b) closest pair

c) network connectivity

d) bipartite matching

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Explanation: Network reliability, connectivity and bipartite matching are all applications of min-cut algorithm whereas closest pair is a different kind of problem.

15. What is the minimum cut of the following network?

a) ({1,3},{4,3},{4,5})

b) ({1,2},{2,3},{4,5})

c) ({1,0},{4,3},{4,2})

d) ({1,2},{3,2},{4,5})

View Answer

Explanation: The minimum cut of the given graph network is found to be ({1,3},{4,3},{4,5}) and its capacity is 23.

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