Minimum Cut MCQ
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
Answer: c
The minimum cut algorithm is solved using the Stoer-Wagner algorithm. The maximum flow problem is solved using the Ford-Fulkerson algorithm. The stable marriage problem is solved using the 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
Answer: a
The minimum cut is a partition of the vertices in 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
Answer: a
The minimum cut algorithm is considered to be an extension of the maximum flow problem. Minimum cut is finding a minimal cut.
4. What does the given figure depict?
a) min-cut problem
b) max cut problem
c) maximum flow problem
d) flow graph
Answer: a
The given figure is a depiction of a 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
Answer: c
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
Answer: c
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|)
Answer: b
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
Answer: b
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
Answer: b
According to the 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 the min-cut problems.
a) Gomory-Hu tree
b) Gomory-Hu graph
c) Dancing tree
d) AA tree
Answer: a
The 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
Answer: b
Gomory-Hu tree can be implemented in two ways- sequential and parallel.
The Gomory–Hu tree of an undirected graph with capacities is a weighted tree that represents the minimum s-t cuts for all s-t pairs in the graph.
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(N2)
Answer: d
The running time of the min-cut algorithm using naïve implementation is mathematically found to be O(N2).
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(N4)
d) O(N2)
Answer: c
The running time of a min-cut algorithm using the Ford-Fulkerson method of making edges birected in a graph is mathematically found to be O(N4).
14. Which one of the following is not an application of the max-flow min-cut algorithm?
a) network reliability
b) closest pair
c) network connectivity
d) bipartite matching
Answer: b
Network reliability, connectivity, and bipartite matching are all applications of the min-cut algorithm whereas the 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})
Answer: a
The minimum cut of the given graph network is found to be ({1,3},{4,3},{4,5}) and its capacity is 23.
