Quiz Space

Advanced Algorithms · End Term · 24 Dec 2023 · September 2023 term · Set ADI4

Question 10: Consider the following bipartite graph: the set A is com…

Question 10

+2 marksOne correct option

You have been given a R × C chessboard, with a list of squares cut out. This problem will involve placing rooks on a chessboard, so that they cannot attack each other. For a rook to attack a target piece, it must share the same row or column as the target.
Find the maximum number of rooks that can be placed on the chessboard, such that no pair of rooks can attack each other.
Rooks cannot be placed on cut out squares. The cut out squares do not affect where the rooks can attack.
Based on the above data, answer the given subquestions.

Consider the following bipartite graph: the set A is composed of elements corresponding to every row of the board, while set B consists of the columns. For each row add edges to every column if the corresponding square is not cut out of the board. What does the answer correspond to in this graph?

  1. A

    the maximum vertex degree

  2. B

    the number of edges in a minimum spanning forest

  3. C

    the size of a maximum matching

  4. D

    none of these

Show answer

Correct answer

  • C

    the size of a maximum matching

See the whole paperTake it as a mock test

Question 10 of 24 in the IIT Madras BS Advanced Algorithms (Advanced Algorithms) End Term paper sat on 24 Dec 2023, in the September 2023 term (IIT M DEGREE FN EXAM FDB1 24 Dec 2023). It carries 2 marks.

This question was also asked in

More questions from this paper

  1. Q1In one term of an academic program, we have n days. Students have to earn at least P credits during these n days to rem…
  2. Q2In one term of an academic program, we have n days. Students have to earn at least P credits during these n days to rem…
  3. Q3In one term of an academic program, we have n days. Students have to earn at least P credits during these n days to rem…
  4. Q4In one term of an academic program, we have n days. Students have to earn at least P credits during these n days to rem…
  5. Q5Figure question
  6. Q6Choose the correct options:
  7. Q7Consider the following instance of Set Cover problem: Universe \mathcal{U} = {a, b, c} Family \mathcal{F} = {S_1 = {a, …
  8. Q8What is the answer if R = C = N and there are no cut out squares?
  9. Q9What is the answer if R = C = N and all the squares on the topmost row and rightmost column (i.e, a L-shape) are cut ou…
  10. Q11What is the maximum number of edges that the graph constructed in the previous question can have?
  11. Q12Consider the following instance of Set Cover problem: Universe \mathcal{U} = {a, b, c, d} Family \mathcal{F} = \left{S_…
  12. Q13Consider the following instance of Set Cover problem: Universe \mathcal{U} = {a, b, c, d} Family \mathcal{F} = \left{S_…
  13. Q14The three-bonaci numbers are defined as follows (please read the definition carefully, as it may not be the generalizat…
  14. Q15The three-bonaci numbers are defined as follows (please read the definition carefully, as it may not be the generalizat…
  15. Q16The three-bonaci numbers are defined as follows (please read the definition carefully, as it may not be the generalizat…
  16. Q17In the MIN-2-SAT problem, we are given a 2-CNF formula \phi and an integer k, and the objective is to decide whether th…
  17. Q18Consider the given statements and answer if they are true or false. The worst-case running time and expected running ti…
  18. Q19Consider the given statements and answer if they are true or false.
  19. Q20Every linear program has a unique optimal solution.
  20. Q21Recall that in the vertex cover problem, we are trying to find a smallest subset S of vertices in a graph G such that G…
  21. Q22Consider the algorithm in the previous question. Does the algorithm always output an optimal vertex cover?
  22. Q23Consider the algorithm in the previous question no 22. Does the algorithm always output a 2- approximate vertex cover?
  23. Q24Recall that the size of an optimal vertex cover is at most twice the size of a maximum matching of a graph G. Are there…